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Abstract: In this paper, sharp two-sided estimates for the transition densities of relativistic α-stable processes with mass in exterior open sets are established for all time . These transition densities are also the Dirichlet heat kernels of with in exterior open sets. The estimates are uniform in m in the sense that the constants are independent of . As a corollary of our main result, we establish sharp two-sided Green function estimates for relativistic α-stable processes with mass in exterior open sets. [Copyright &y& Elsevier]

Abstract: We give upper and lower bounds of perturbation series for transition densities, corresponding to additive gradient perturbations satisfying certain space–time integrability conditions. [Copyright &y& Elsevier]

Abstract: We consider a stochastic volatility model with Lévy jumps for a log-return process of the form , where is a classical stochastic volatility process and is an independent Lévy process with absolutely continuous Lévy measure . Small-time expansions, of arbitrary polynomial order, in time-, are obtained for the tails , , and for the call-option prices , , assuming smoothness conditions on the density of away from the origin and a small-time large deviation principle on . Our approach allows for a unified treatment of general payoff functions of the form for smooth functions and . As a consequence of our tail expansions, the polynomial expansions in of the transition densities are also obtained under mild conditions. [Copyright &y& Elsevier]

The Poisson-TrEsp method (where TrEsp stands for transition charges from electrostatic potentials) has been successfully applied to calculate excitonic couplings in a variety of pigment-protein complexes. It relies on an isomorphism that allows for relating the excitonic coupling between transition densities in dielectric media to their Coulomb coupling. This isomorphism was derived by Hsu et al. (J. Chem. Phys. 114, 3065, (2001)) using time-dependent density functional response theory. In this article, we provide an alternative and simple derivation by first-order perturbation theory. An application of Poisson-TrEsp to photosystem I trimers reveals that the local field correction/screening factor depends on the mutual orientation of the pigments and on the dielectric boundaries rather than on distance. A mean correction factor of f = 0.69 is determined for this system. [ABSTRACT FROM AUTHOR]

In this paper, by using probabilistic methods, we establish sharp two-sided large time estimates for the transition densities of relativistic α-stable processes with mass m ∈ (0, 1] (i.e., for the Dirichlet heat kernels of m − ( m − Δ) with m ∈ (0, 1]) in half-space-like C open sets. The estimates are uniform in m in the sense that the constants are independent of m ∈ (0, 1]. Combining with the sharp two-sided small time estimates, established in Chen et al. (Ann Probab, ), valid for all C open sets, we have now sharp two-sided estimates for the transition densities of relativistic α-stable processes with mass m ∈ (0, 1] in half-space-like C open sets for all times. Integrating the heat kernel estimates with respect to the time variable, one can recover the sharp two-sided Green function estimates for relativistic α-stable processes with mass m ∈ (0, 1] in half-space-like C open sets established recently in Chen et al. (Stoch Process their Appl, ). [ABSTRACT FROM AUTHOR]

We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps. [ABSTRACT FROM AUTHOR]

This article describes three methods for computing a discrete joint density from full conditional densities. They are the Gibbs sampler, a hybrid method, and an interaction-based method. The hybrid method uses the iterative proportional fitting algorithm, and it is derived from the mixed parameterization of a contingency table. The interaction-based approach is derived from the canonical parameters, while the Gibbs sampler can be regarded as based on the mean parameters. In short, different approaches are motivated by different parameterizations. The setting of a bivariate conditionally specified distribution is used as the premise for comparing the numerical accuracy of the three methods. Detailed comparisons of marginal distributions, odds ratios and expected values are reported. We give theoretical justifications as to why the hybrid method produces better approximation than the Gibbs sampler. Generalizations to more than two variables are discussed. In practice, Gibbs sampler has certain advantages: it is conceptually easy to understand and there are many software tools available. Nevertheless, the hybrid method and the interaction-based method are accurate and simple alternatives when the Gibbs sampler results in a slowly mixing chain and requires substantial simulation efforts. [ABSTRACT FROM AUTHOR]

Likelihood-based inference for parameters of stochastic differential equation (SDE) models is challenging because for most SDEs the transition density is unknown. We propose a method for estimating the transition density that involves expanding the sample path as an Ito-Taylor series, calculating the moment generating function of the retained terms in the Ito-Taylor expansion, then employing a saddlepoint approximation. We perform a numerical comparison with two other methods similarly based on small-time expansions and discuss the pros and cons of our new method relative to other approaches. [ABSTRACT FROM AUTHOR]

In this paper, due to the effect of positively-charged screening holes, Coulomb potential energy 1/r is modified to be 1/rp, which is assumed to deviate slightly from the former. Using many-body perturbation theory, we obtain a simple analytic representation of the ground-state energy and correlation energy for a uniform electron gas. Our results agree with those obtained by the numerical and semi-analytic methods at low-density limit. Higher ground-state energies at high-density limit are calculated from our model. High order r expansion terms are found at high-density region. A curve of transition density versus p is drawn via the Misawa spin-scaling relation, which is in consistent with Perdew's study at low-density limit. [ABSTRACT FROM AUTHOR]

In this paper, due to the effect of positively-charged screening holes, Coulomb potential energy 1/r is modified to be 1/rp, which is assumed to deviate slightly from the former. Using many-body perturbation theory, we obtain a simple analytic representation of the ground-state energy and correlation energy for a uniform electron gas. Our results agree with those obtained by the numerical and semi-analytic methods at low-density limit. Higher ground-state energies at high-density limit are calculated from our model. High order r expansion terms are found at high-density region. A curve of transition density versus p is drawn via the Misawa spin-scaling relation, which is in consistent with Perdew's study at low-density limit. [ABSTRACT FROM AUTHOR]

Abstract: Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding Lévy measure and the Lévy–Khinchin exponent. [Copyright &y& Elsevier]

We consider the problem of parameter estimation for an ergodic diffusion with Fisher-Snedecor invariant distribution, to be called Fisher-Snedecor diffusion. We propose moments-based estimators of unknown parameters, based on both discrete and continuous observations, and prove their consistency and asymptotic normality. The explicit form of the asymptotic covariance matrix is determined by using the properties of eigenfunctions (Fisher-Snedecor polynomials) of the corresponding Sturm-Liouville operator. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the initial value problem for a class of non-linear stochastic equations of Burgers type of the following form for , where is a pseudo-differential operator with negative definite symbol of variable order which generates a stable-like process with transition density, are measurable functions, and stands for a Lévy space-time white noise. We investigate the stochastic equation on the whole space in the mild formulation and show the existence of a unique local mild solution to the initial value problem by utilising a fixed point argument. [ABSTRACT FROM AUTHOR]

We consider the fractional Laplacian --(--Δ)α/2 on an open subset in ℝd with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian in C1,1 open sets. This heat kernel is also the transition density of a rotationally symmetric α-stable process killed upon leaving a C1,1 open set. Our results are the first sharp two-sided estimates for the Dirichlet heat kernel of a non-local operator on open sets. [ABSTRACT FROM AUTHOR]

We consider Feller semigroups with jump intensity dominated by that of the rotation invariant stable Lévy process. Using an approximation scheme we obtain estimates of corresponding heat kernels. [ABSTRACT FROM AUTHOR]

In this paper, we study the precise behavior of the transition density functions of censored (resurrected) α-stable-like processes in C1,1 open sets in $${\mathbb R^d}$$ , where d ≥ 1 and $${\alpha\in (1, 2)}$$ . We first show that the semigroup of the censored α-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functions of a large class of censored α-stable-like processes in C1,1 open sets. We further obtain sharp two-sided estimates for the Green functions of these censored α-stable-like processes in bounded C1,1 open sets. [ABSTRACT FROM AUTHOR]

This study presents diffusion processes methodology on tree diameter distribution problem. We use stochastic differential equation methodology to derive a univariate age-dependent probability density function of a tree diameter distribution. The purpose of this paper is to investigate the relationship between the stochastic linear and logistic shape diameter growth models and diameter distribution laws. We establish the probabilistic characteristics of stochastic growth models, such as the univariate transition probability density of tree diameter, the mean and variance of tree diameter. We carry out comparison of proposed continuous time stochastic models on the basis of Hong-Li, Gini, Shapiro-Wilk goodness-of-fit statistics and normal probability plot. Parameter estimations are based on discrete observations over age of trees. To model the tree diameter distribution, as an illustrative experience, a real data set from repeated measurements on a permanent sample plot of pine (Pinus sylvestris) stand in the Kazlu Ruda district at Lithuania is used. The results are implemented in the symbolic computational language MAPLE. [ABSTRACT FROM AUTHOR]

We develop a specification test for the transition density of a discretely sampled continuous-time jump-diffusion process, based on a comparison of a nonparametric estimate of the transition density or distribution function with their corresponding parametric counterparts assumed by the null hypothesis. As a special case, our method applies to pure diffusions. We provide a direct comparison of the two densities for an arbitrary specification of the null parametric model using three different discrepancy measures between the null and alternative transition density and distribution functions. We establish the asymptotic null distributions of proposed test statistics and compute their power functions. We investigate the finite-sample properties through simulations and compare them with those of other tests. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

Penta-, hexa-, and heptaacetonitrile complexes of divalent cations of the first transition series are studied by ab initio molecular orbital calculations. The factors that determine the structural stability and the reaction mechanism of solvent-exchange reactions are discussed. All the penta- and hexaacetonitrile species are at local minima, whereas the geometrical stability of the heptacoordinated species depends on the 3d electron configurations. The structural stability of heptaacetonitrile species is intermediate between those of hydrogen cyanide complexes and hydrates. Acetonitrile exchange reactions have more dissociative character than hydrogen cyanide exchange reactions because the inductive effect of the methyl group in CH3CN destabilizes the heptacoordinated structures. The successive binding energies show that associative mechanisms are favorable for acetonitrile exchange with earlier members of the first transition series, whereas dissociative mechanisms become favorable for later members. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a data augmentation technique for statistical inference concerning stochastic cusp catastrophe model subject to missing data and partially observed observations. We propose a Bayesian inference solution that naturally treats missing observations as parameters and we validate this novel approach by conducting a series of Monte Carlo simulation studies assuming the cusp catastrophe model as the underlying model. We demonstrate that this Bayesian data augmentation technique can recover and estimate the underlying parameters from the stochastic cusp catastrophe model. [ABSTRACT FROM AUTHOR]

Abstract: For an arbitrary Hilbert space-valued Ornstein–Uhlenbeck process we construct the Ornstein–Uhlenbeck bridge connecting a given starting point and an endpoint provided belongs to a certain linear subspace of full measure. We derive also a stochastic evolution equation satisfied by the OU bridge and study its basic properties. The OU bridge is then used to investigate the Markov transition semigroup defined by a stochastic evolution equation with additive noise. We provide an explicit formula for the transition density and study its regularity. These results are applied to show some basic properties of the transition semigroup. Given the strong Feller property and the existence of invariant measure we show that all functions are transformed into continuous functions, thus generalising the strong Feller property. We also show that transition operators are -summing for some , in particular of Hilbert–Schmidt type. [Copyright &y& Elsevier]

An expression of unexpected simplicity is derived for the shift in optical transition energies of solute molecules in nonpolar solvents. The expression reveals a new spectroscopic rule that says: The higher the excited state of the solute, the larger the solvatochromic red shift. A puzzle formulated >50 years ago by Bayliss is solved. Bayliss, based on arguments from classical physics, assumed that the shift scales with the oscillator strength of the solute transition, but noted strong quantitative deviations from this rule in experiments. As the present expression shows, the shift does not depend on the oscillator strength of the transition, but reflects the change in dispersive solute-solvent interactions between the ground and excited states of the solute, that are determined by the anisotropy of intramolecular electron correlation. The theory is applied to explain the solvatochromic shifts of the two lowest electronic excitations of bacteriochlorophyll a and bacteriopheophytin a. [ABSTRACT FROM AUTHOR]

Abstract: The ground and excited-state properties of oligothiophenes connected by Si-atoms have been studied theoretically, based on recent experimental reports [M. Fujitsuka, D.W. Cho, J. Ohshita, A. Kunai, T. Majima, J. Phys. Chem. C 111 (2007) 1993]. Herein, we have employed a density-functional theory (DFT) approach toward examining the influence of the number of oligothiophenes on molecular ground-state properties, focusing on the density of state and the density distribution on the subunit of the oligothiophenes. Furthermore, we have investigated several excited-state properties of these oligothiophene. We discuss absorption with transition densities, which reveal the orientations and strengths of transition dipole moments, charge difference densities, which allow for the study of transition dipole moments and charge transfer in the absorption processes, and transition density matrices, which provide information about the electron–hole coherence and excitation delocalization. All of these properties were studied by employing time-dependent density functional theory (TD-DFT). Our theoretical results indicate that there are not only localized excited states, but also inter-branched charge transfer excited states in absorption for block copolymers of the oligothiophenes. In all, the theoretical analyses provide insight into the ground- and excited-state properties of the polymers, notably on the hopping mechanism of charge transfer in blocked oligothiophenes by Si atoms. [Copyright &y& Elsevier]

Abstract: We study the following model of hidden Markov chain: with a real-valued positive recurrent and stationary Markov chain, and a noise independent of the sequence having a known distribution. We present an adaptive estimator of the transition density based on the quotient of a deconvolution estimator of the density of and an estimator of the density of . These estimators are obtained by contrast minimization and model selection. We evaluate the risk and its rate of convergence for ordinary smooth and supersmooth noise with regard to ordinary smooth and supersmooth chains. Some examples are also detailed. [Copyright &y& Elsevier]

Abstract: For with each being a signed measure on belonging to the Kato class , a diffusion with drift is a diffusion process in whose generator can be formally written as where is a uniformly elliptic differential operator. When each is given by for some function , a diffusion with drift is a diffusion in with generator . In [P. Kim, R. Song, Two-sided estimates on the density of Brownian motion with singular drift, Illinois J. Math. 50 (2006) 635–688; P. Kim, R. Song, Boundary Harnack principle for Brownian motions with measure-valued drifts in bounded Lipschitz domains, Math. Ann., 339 (1) (2007) 135–174], we have already studied properties of diffusions with measure-valued drifts in bounded domains. In this paper we first show that the killed diffusion process with measure-valued drift in any bounded domain has a dual process with respect to a certain reference measure. We then discuss the potential theory of the dual process and Schrödinger-type operators of a diffusion with measure-valued drift. More precisely, we prove that (1) for any bounded domain, a scale invariant Harnack inequality is true for the dual process; (2) if the domain is bounded , the boundary Harnack principle for the dual process is valid and the (minimal) Martin boundary for the dual process can be identified with the Euclidean boundary; and (3) the harmonic measure for the dual process is locally comparable to that of the -conditioned Brownian motion with being an eigenfunction corresponding to the largest Dirichlet eigenvalue in the domain. The Schrödinger operator that we consider can be formally written as where is uniformly elliptic, is a vector-valued signed measure on and is a signed measure in . We show that, for a bounded Lipschitz domain and under the gaugeability assumption, the (minimal) Martin boundary for the Schrödinger operator obtained from the diffusion with measure-valued drift can be identified with the Euclidean boundary. [Copyright &y& Elsevier]

Abstract: In this paper, we study first the problem of nonparametric estimation of the stationary density of a discrete-time Markov chain . We consider a collection of projection estimators on finite dimensional linear spaces. We select an estimator among the collection by minimizing a penalized contrast. The same technique enables us to estimate the density of and so to provide an adaptive estimator of the transition density . We give bounds in norm for these estimators and we show that they are adaptive in the minimax sense over a large class of Besov spaces. Some examples and simulations are also provided. [Copyright &y& Elsevier]

Abstract: We present new, generally applicable protocols for the computation of the coupling parameter, J, of excitation energy transfer with quantum chemical ab initio methods. The protocols allow to select the degree of approximation and computational demand such that they are applicable for realistic systems and still allow to control the quality of the approach. We demonstrate the capabilities of the different protocols using the CO dimer as a first example. Correlation effects are found to scale J by a factor of about 0.7 which is in good agreement to earlier results obtained for the ethene dimer. The various levels of the protocol allow to assess the influence of ionic configurations and the polarisation within the dimer. Further, the interplay between the Förster and Dexter contribution to J is investigated. The computations also show error compensation within approximations that are widely used for extended systems as in particular the transition density cube method. [Copyright &y& Elsevier]

Discretized simulation is widely used to approximate the transition density of discretely observed diffusions. A recently proposed importance sampler, namely modified Brownian bridge, has gained much attention for its high efficiency relative to other samplers. It is unclear for this sampler, however, how to balance the trade-off between the number of imputed values and the number of Monte Carlo simulations under a given computing resource. This paper provides an asymptotically efficient allocation of computing resource to the importance sampling approach with a modified Brownian bridge as importance sampler. The optimal trade-off is established by investigating two types of errors: Euler discretization error and Monte Carlo error. The main results are illustrated with two simulated examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a new estimator for the transition density π of an homogeneous Markov chain is considered. We introduce an original contrast derived from regression framework and we use a model selection method to estimate π under mild conditions. The resulting estimate is adaptive with an optimal rate of convergence over a large range of anisotropic Besov spaces . Some simulations are also presented. [Copyright &y& Elsevier]

This article focuses on two methods to approximate the log-likelihood of discretely observed univariate diffusions: (1) the simulation approach using a modified Brownian bridge as the importance sampler, and (2) the closed-form approximation approach. For the case of constant volatility, we give a theoretical justification of the modified Brownian bridge sampler by showing that it is exactly a Brownian bridge. We also discuss computational issues in the simulation approach such as accelerating the numerical variance stabilizing transformation, computing derivatives of the simulated log-likelihood, and choosing initial values of parameter estimates. The two approaches are compared in the context of financial applications under a benchmark model which has an unknown transition density and has no analytical variance stabilizing transformation. The closed-form approximation, particularly the second-order closed-form, is found to be computationally efficient and very accurate when the observation frequency is monthly or higher. It is more accurate in the center than in the tails of the transition density. The simulation approach combined with the variance stabilizing transformation is found to be more reliable than the closed-form approximation when the observation frequency is lower. Both methods perform better when the volatility level is lower, but the simulation method is more robust to the volatility level. When applied to two well-known datasets of daily observations, the two methods yield similar parameter estimates in both datasets but slightly different log-likelihoods in the case of higher volatility. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a conditional gauge theorem for these diffusions in bounded Lipschitz domains. Informally the Schrödinger-type operators we consider are of the form where L is a uniformly elliptic second order differential operator, μ is a vector-valued signed measure belonging to and ν is a signed measure belonging to . In this paper, we establish two-sided estimates for the heat kernels of Schrödinger-type operators in bounded -domains and a scale invariant boundary Harnack principle for the positive harmonic functions with respect to Schrödinger-type operators in bounded Lipschitz domains. [Copyright &y& Elsevier]

The Dirichlet process mixture of normal densities has been successfully used as a prior for Bayesian density estimation for independent and identically distributed (i.i.d.) observations. A Markov model, which generalizes the i.i.d. set up, may be thought of as a suitable framework for observations arising over time. The predictive density of the future observation is then given by the posterior expectation of the transition density given the observations. We consider a Dirichlet process mixture prior for the transition density and study posterior consistency. Like the i.i.d. case, posterior consistency is obtained if the Kullback–Leibler neighborhoods of the true transition density receive positive prior probabilities and uniformly exponentially consistent tests exist for testing the true density against the complement of its neighborhoods. We show that under reasonable conditions, the Kullback–Leibler property holds for the Dirichlet mixture prior. For certain topologies on the space of transition densities, we show consistency holds under appropriate conditions by constructing the required tests. This approach, however, may not always lead to the best possible results. By modifying a recent approach of Walker [2004. New approaches to Bayesian consistency. Ann. Statist. 32, 2028–2043] for the i.i.d. case, we also show that better conditions for consistency can be given for certain weaker topologies. [Copyright &y& Elsevier]

Abstract: Excited state properties of novel p- and n-type organic semiconductors with a thiazolothiazole unit are theoretically investigated with quantum chemical methods. The calculated absorption frequencies of them are consistent with the experimental data. The dihedral angles between the thiazolothiazole unit and the trifluoromethylphenyl (or thiophene) are examined from the optimized geometries at ground states. To study the influence of the individual units of the derivatives to the excited state properties of them, the energies and densities of frontier orbital HOMOs and LUMOs of the individual unit and the derivatives are investigated in the absorption processes. The excited properties of the two derivatives are studied with 2D and 3D real-space analysis methods, which are employed to study the electron–hole coherence and the excitation delocalization (with transition density matrix method), and charge and energy transfer (with transition and charge difference density method). The insights of the optical electron properties of the semiconductor in the absorption are revealed theoretically. [Copyright &y& Elsevier]

Accurate quantum computational chemistry has evolved dramatically. The size of molecular systems, which can be studied accurately using molecular theory, is increasing very rapidly. Theoretical chemistry has opened up a world of new possibilities. It can treat real systems with predictable accuracy. Computational chemistry is becoming an integral part of theoretical and experimental research in chemical science. In this paper, we will review our recent developments in the theoretical and computational study on some very interesting subjects such as fluorescent fluoride sensor, "on–off" molecular switch, electron transport through π-stacking, and molecular electronic device on the basis of the molecular functional levels. We provide a brief introduction about the importance of all these systems in the present scenario of scientific activity and the numerical results and discussion in the light of experimentally found results. We have enjoyed good progress in each of the above areas. We are very excited about our discoveries in each field and would like to share this enthusiasm with readers. [ABSTRACT FROM AUTHOR]

A new binaphthalene molecule with two spiropyran units used for chiral molecular switches and logic gates was synthesized and characterized.12 In this paper, charge and energy transfer in binaphthalene molecule with two spiropyran units are theoretically investigated with quantum chemistry method, as well as 2D and 3D real space analysis methods, since molecule construction with photoinduced electron transfer or charge transfer is one of the most frequently used pathways for building useful sensors and molecular machines. The orientation and strength of transition dipole moment in absorption spectra are obtained by 3D transition density. The orientation and results of intramolecular charge transfer on the excitation are obtained with 3D charge difference densities. The electron-hole coherence and excitation delocalization in absorption spectra are investigated with 2D contour plots of transition density matrix. Overall, the computed results remain in good agreement with the relevant experimental data, and the theoretical results reveal the relationship between the function of sensor and the excited state properties of the structure and transformation of the compound, upon addition of acid and base in absorption spectra. [ABSTRACT FROM AUTHOR]

In this paper, we first study a purely discontinuous Girsanov transform which is more general than that studied in Chen and Song [(2003), J. Funct. Anal. 201, 262–281]. Then we show that the transition density of any purely discontinuous Girsanov transform of a symmetric stable process is comparable to the transition density of the symmetric stable process. The same is true for the Girsanov transform introduced in Chen and Zhang [(2002), Ann. Inst. Henri poincaré 38, 475–505]. As an application of these results, we show that the Green function of Feynman–Kac type transforms of symmetric stable processes by continuous additive functionals of zero energy, when exists, is comparable to that of the symmetric stable process. [ABSTRACT FROM AUTHOR]

This paper describes methods for formulating and estimating system reliability in settings where failure results from wear of system parts reaching a critical threshold. We propose a model concerned with the stochastic behavior of wear in which a right-continuous non-decreasing wear process is composed of “continuous” and “jump” parts. Several properties of our proposed model are presented, bounds are obtained for the reliability function, and the unknown parameters are estimated by the method of maximum likelihood. From these an estimate of the reliability function is obtained. In this part, contrary to common practice, we do not assume availability of failure data. [ABSTRACT FROM AUTHOR]

This paper gives a brief overview of the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inference for instantaneous returns and volatility functions of time-homogeneous and time-dependent diffusion processes, and estimation of transition densities and state price densities. We first briefly describe the problems and then outline the main techniques and main results. Some useful probabilistic aspects of diffusion processes are also briefly summarized to facilitate our presentation and applications. [ABSTRACT FROM AUTHOR]

We extend the idea of crossvalidation to choose the smoothing parameters of the ‘double-kernel’ local linear regression for estimating a conditional density. Our selection rule optimises the estimated conditional density function by minimising the integrated squared error. We also discuss three other bandwidth selection rules, an ad hoc method used by Fan et al. (1996), a bootstrap method of Hall et al. (1999) for bandwidth selection in the estimation of conditional distribution functions, modified by Bashtannyk & Hyndman (2001) to cover conditional density functions, and finally a simple approach proposed by Hyndman & Yao (2002). The performance of the new approach is compared with these three methods by simulation studies, and our method performs outstandingly well. The method is illustrated by an application to estimating the transition density and the Value-at-Risk of treasury-bill data. [ABSTRACT FROM AUTHOR]

Let X be the diffusion Markov process on Rd with the generator L=1/2∑i,j=1daij(x)∂xixj2+∑i=1dbi(x)∂xi, and transition density G(t,x,y). Under some conditions on the matrix a(x) we get the estimate sup0 for all T>0. The latter estimate is used to get the existence and uniqueness of a solution of the following gas system: where ρ0(dx) (a probability measure on Rd), and the bounded vector field v:=(v1,…,vd) :Rd→Rd are given. The family of probability measures ρ:=ρ(dx,t) and the velocities u:=u(x,t) are unknown. Here L* is the formal adjoint operator of L. [Copyright &y& Elsevier]

Models in economics and other fields often require a restricted Brownian motion because frequently implicit or explicit barriers restrict the domain. This paper contributes to the literature on reflected Brownian motion by deriving its conditional density function as a closed-form expression that consists of infinite sums of Gaussian densities. This solution is compared with an alternative, trigonometric expression derived earlier. Numerical analyses reveal that convergence properties of the expression derived in this paper are superior to those of the alternative representation for most practically relevant set-ups. Despite the complex appearance of the density formula, its use only requires fractions of a second on simple desktop computers such that, next to the theoretical appeal, also practicability is guaranteed. [ABSTRACT FROM AUTHOR]

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The octupole strengths of three nuclei: β-stable nucleus 20882Pb126, neutron skin nucleus 6020Ca40 and neutron drip line nucleus 288O20 are studied by using the self-consistent Hartree–Fock calculation with the random phase approximation. The collective properties of low-lying excitations are analyzed by particle–vibration coupling. The results show that there is the coexistence of the collective excitations and the decoupled strong continuum strength near the threshold in the lowest isoscalar states in 6020Ca40 and 288O20. For these three nuclei, both the low-lying isoscalar states and giant isoscalar resonance carry isovector strength. The ratio B(IV)/B(IS) is checked and it is found that, for 20882Pb126, the ratio is equal to ((N−Z)/A)2 in good accuracy, while for 6020Ca40 and 288O20, the ratios are much larger than ((N−Z)/A)2. The study shows that the enhancement of the ratio is due to the excess neutrons that have small binding energies in 6020Ca40 and 288O20. [Copyright &y& Elsevier]

When a continuous‐time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observations is not explicitly computable. Using Hermite polynomials, I construct an explicit sequence of closed‐form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and shares its asymptotic properties. Monte Carlo evidence reveals that this method outperforms other approximation schemes in situations relevant for financial models. [ABSTRACT FROM AUTHOR]