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In this paper, we discuss estimates on the transition densities of subordinators, which are global in time. We establish sharp two-sided estimates on the transition densities of subordinators whose Lévy measures are absolutely continuous and decaying in mixed polynomial orders. Under a weaker assumption on Lévy measures, we also obtain precise asymptotic behaviors of the transition densities at infinity. Our results cover geometric stable subordinators, Gamma subordinators and much more. [ABSTRACT FROM AUTHOR]

In this paper we discuss non-local operators with killing potentials, which may not be in the standard Kato class. We first discuss factorization of their Dirichlet heat kernels in metric measure spaces. Then we establish explicit estimates of the Dirichlet heat kernels under critical killings in C 1 , 1 open subsets of R d or in R d ∖ { 0 }. The decay rates of our explicit estimates come from the values of the multiplicative constants in the killing potentials. Our method also provides an alternative and unified proof of the main results of [18–20]. [ABSTRACT FROM AUTHOR]

We consider a large class of symmetric pure jump Markov processes dominated by isotropic unimodal Lévy processes with weak scaling conditions. First, we establish sharp two-sided heat kernel estimates for these processes in C 1 , 1 open sets. As corollaries of our main results, we obtain sharp two-sided Green function estimates and a scale invariant boundary Harnack inequality with explicit decay rates in C 1 , 1 open sets. [ABSTRACT FROM AUTHOR]

Quenched and annealed heat kernel estimates are established for Fontes–Isopi–Newman (FIN) processes on spaces equipped with a resistance form. These results are new even in the case of the one-dimensional FIN diffusion, and also apply to fractals such as the Sierpinski gasket and carpet. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an efficient stochastic method for solving space-fractional diffusion equations in high dimensions based on the Feynman–Kac formula. The key idea is to approximate the trajectory of the process by using a series of balls. As an extension of our first work Sheng et al. (2022) for the Poisson equation, the new algorithm finds remarkably efficient in solving time-dependent linear problems with integral fractional Laplacian on the bounded and unbounded domains. We present some numerical examples to validate the robustness and efficiency of our methods. [ABSTRACT FROM AUTHOR]

In this paper, we establish the precise asymptotic behaviors of the tail probability and the transition density of a large class of isotropic Lévy processes when the scaling order is between 0 and 2 including 2 . We also obtain the precise asymptotic behaviors of the tail probability of subordinators when the scaling order is between 0 and 1 including 1 . The asymptotic expressions are given in terms of the radial part of characteristic exponent ψ and its derivative. In particular, when ψ ( λ ) − λ 2 ψ ′ ( λ ) varies regularly, as t ψ ( r − 1 ) 2 ψ ( r − 1 ) − ( 2 r ) − 1 ψ ′ ( r − 1 ) → 0 the tail probability – ( | X t | ≥ r ) is asymptotically equal to a constant times t ( ψ ( r − 1 ) − ( 2 r ) − 1 ψ ′ ( r − 1 ) ) . [ABSTRACT FROM AUTHOR]

For the recently developed particle–hole dispersive optical model, weak violations of unitarity due to a phenomenological description of the spreading effect are considered. Methods for unitarity restoration are proposed and implemented for the 208 Pb nucleus in the description of the energy-averaged isoscalar monopole double transition density and strength functions in a wide excitation energy interval that includes the isoscalar giant monopole resonance and its overtone. To illustrate abilities of the model, direct neutron decay of the mentioned giant resonance is also considered. [ABSTRACT FROM AUTHOR]

We define heavy-tailed fractional reciprocal gamma and Fisher–Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher–Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher–Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation. [ABSTRACT FROM AUTHOR]

Details of charge density distribution at p-n nano interface are analyzed with density functional theory techniques using model system of dimers of doped silicon quantum dots interacting through bond and through space . Spatial distributions of transition densities between the ground and excited states suggest the character of essential electronic excitations, which have a Fӧrster, bound, unbound, or charge transfer character. A redistribution of electronic density from n-impurities to p-impurities results in a ground state polarization and creates an offset of energies of the bands localized on p-doped quantum dot and the bands localized on n-doped quantum dot. Although impurities contribute very few orbitals to the total density, a ground state charge redistribution and polarization are both responsible for the presence of a large number of charge transfer excitations involving solely silicon orbitals. [ABSTRACT FROM AUTHOR]

The particle–hole dispersive optical model, developed recently, is applied to study properties of high-energy isoscalar monopole excitations in medium-heavy mass spherical nuclei. The energy-averaged strength functions of the isoscalar giant monopole resonance and its overtone in 208 Pb are analyzed. In particular, we analyze the energy-averaged isoscalar monopole double transition density, the key quantity in the description of the hadron–nucleus inelastic scattering, and studied the validity of the factorization approximation using semi classical and microscopic one body transition densities, respectively, in calculating the cross sections for the excitation of isoscalar giant resonances by inelastic alpha scattering. [ABSTRACT FROM AUTHOR]

Motivated by the close connection between the skew Brownian motion and the random particle motion in heterogeneous media, we investigate the reflected skew Brownian motion and try to find out its relationship with the corresponding dispersion problem when there exists a reflecting boundary. Through the use of the knowledge of stochastic analysis, we provide some basic properties of reflected skew Brownian motions, including the transition density, the Laplace transform of the first passage time, and some related results. A simple method to generate the sample path is also proposed. At the end of this paper, we reveal the strong relationship between the reflected skew Brownian motion and the solute dispersion in the presence of a sharp interface and a reflecting boundary. [ABSTRACT FROM AUTHOR]

Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness for a large class of subordinate killed Brownian motions in bounded C 1 , 1 domains, C 1 , 1 domains with compact complements and domains above graphs of bounded C 1 , 1 functions. [ABSTRACT FROM AUTHOR]

For α ∈ ( 0 , 2 ) and M > 0 , we consider a family of nonlocal operators { Δ + a α Δ α / 2 , a ∈ ( 0 , M ] } on R d under Kato class gradient perturbation. We establish the existence and uniqueness of their fundamental solutions, and derive their sharp two-sided estimates. The estimates give explicit dependence on a and recover the sharp estimates for Brownian motion with drift as a → 0 . Each fundamental solution determines a conservative Feller process X . We characterize X as the unique solution of the corresponding martingale problem as well as a Lévy process with singular drift. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study sharp Dirichlet heat kernel estimates for a large class of symmetric Markov processes in open sets. The processes are symmetric pure jump Markov processes with jumping intensity , where . Here, is an increasing function on , with on and on for , and is a symmetric function confined between two positive constants, with for and . We establish two-sided estimates for the transition densities of such processes in open sets when . In particular, our result includes (relativistic) symmetric stable processes and finite-range stable processes in open sets when . [Copyright &y& Elsevier]

Abstract: Suppose that and . Let be such that each is a signed measure on belonging to the Kato class . In this paper, we consider the stochastic differential equation where is a symmetric -stable process on and for each , the th component of is a continuous additive functional of finite variation with respect to whose Revuz measure is . The unique solution for the above stochastic differential equation is called an -stable process with drift . We prove the existence and uniqueness, in the weak sense, of such an -stable process with drift and establish sharp two-sided heat kernel estimates for such a process. [Copyright &y& Elsevier]

Abstract: In order to clarify the origin of the excited state properties gained by time-dependent density functional theory (TDDFT) with various functionals, we investigate them in terms of the orbital- and density-based properties: natural transition orbitals (NTO), transition density (TD), and charge difference density (CDD). We focus on the spectra of N-phenylpyrrole: a molecule in which the charge transfer (CT) excitations are included in its excited states. As a reference, we also analyze the spectra of naphthalene: a molecule whose excited states are characterized with local excitations (LE). Throughout the analyses with NTO, TD and CDD, we clarify the distinguished nature of the CT spectra and its origin gained by the long range corrected (LC) TDDFT. [Copyright &y& Elsevier]

Abstract: We consider the problem of testing the hypothesis on marginal distribution of ergodic diffusion with Fisher–Snedecor invariant distribution, to be called Fisher–Snedecor diffusion. We propose a GMM approach to testing this statistical hypothesis where the moment condition is based on eigenfunctions of the diffusion infinitesimal generator—Fisher–Snedecor polynomials. Statistical test is observed in two different settings: (1) for known values of parameters of the process; (2) for consistent moment based estimators of parameters. Results are illustrated in a short simulation study. [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]

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]

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]

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]

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: 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]

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]

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]

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]

In this paper, we study a reflected constant elasticity of variance (RCEV) process with two-sided reflecting barriers for modeling the dynamics of a foreign exchange rate in a target zone. We derive a closed form expression for the transition density by using the spectral expansion method. Monte Carlo simulation shows that our method is accurate and efficient when the results are applied to compute the expected value of the process. Finally, we illustrate that ignoring target zones in the CEV model may lead to significant computational errors. • The dynamics of exchange rates in target zones is modeled by the RCEV process. • Transition density of the process is derived by spectral expansion method. • Monte Carlo simulation shows that our method is accurate and efficient. • Ignoring target zones in the CEV model may lead to significant computational errors. [ABSTRACT FROM AUTHOR]