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Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi‐closed form expressions of the term structure of risks. We introduce the class of noncausal affine linear factor models by considering factors that are affine in reverse time. These models are especially relevant for pricing sequences of speculative bubbles. We show that they feature nonaffine dynamics in calendar time, while still providing (quasi) closed form term structures and derivative pricing formulas. The framework is illustrated with term structure of interest rates and European call option pricing examples. [ABSTRACT FROM AUTHOR] more...

Compared with single-component seismic data, multicomponent seismic data contain more P- and S-wave information. Making full use of multicomponent seismic data can improve the accuracy of seismic exploration. Elastic reverse-time migration (ERTM) is the most advanced migration technology for imaging multicomponent seismic data from complex subsurface structures. However, most conventional ERTM methods often use the adjoint operator of forward operator for approximation to the inverse operator. When the multicomponent seismic data suffer from a finite recording aperture, limited bandwidth, and imperfect illumination, the image quality of conventional ERTM is greatly reduced. In this study, we propose an elastic least-squares reverse-time migration (ELSRTM) scheme to improve the image quality of ERTM through multiple iterations. We first review the ERTM method; then, we derive the Born modeling equations, adjoint wave equations, and gradient equations of P- and S-wave images of ELSRTM. The new gradient equations, which use the time derivative of stress to replace the spatial derivative of particle velocity for improving the accuracy of gradients near the boundary, are also proposed. We compare the performance of ERTM with ELSRTM via synthetic experiments in numerical examples. Synthetic examples reveal that ELSRTM can generate high-quality images with higher resolution, fewer artifacts, and more balanced amplitude than ERTM. [ABSTRACT FROM AUTHOR] more...

For the high-precision seismic imaging of complex structures on irregular topographies, this study proposes a Chebyshev spectral-element reverse time migration (CSE-RTM) method coupled with the implicit Newmark time integral method. The approach is first applied to a numerical example to consider factors affecting numerical accuracy, such as the time step and the pattern of subdivision of the computational domain. The results show that the smaller the time step is, the higher the numerical accuracy is and that numerical accuracy improves when the grid nodes tend to be distributed uniformly in the computational domain. The spectral element method combines the advantages of the stronger boundary-related adaptability of the finite element method with the high accuracy and fast convergence of the spectral method. This method is applied to reverse time migration imaging, and tests of the model show that its accuracy of imaging is higher than that of the conventional finite-difference reverse time migration method in case of complex structures in areas with irregular topography. To improve the efficiency of parallel computing of the CSE-RTM, an iterative algorithm is proposed to solve the hierarchical equilibrium sparse linear equations (HELPs) for it based on the idea of the degrees of cohesion of freedom and local relaxation. This algorithm has the advantage that the efficiency of parallel computation does not decrease with an increasing number of processors while the number of iterations required for convergence is controlled. Owing to the fast convergence of the spectral method on a sparse grid coupled with the parallel computational scheme of HELPs, the efficiency of calculation of the CSE-RTM is significantly improved. [ABSTRACT FROM AUTHOR] more...

In comparison with conventional reverse time migration (RTM), least-squares RTM (LSRTM) can improve imaging resolution and compensate irregular illumination caused by acquisition geometry and complex structures. Since proposed, as an advanced version of RTM, it has been applied a lot to improve resolution and balance amplitude in imaging. Generally, in LSRTM, there are two kinds of LSRTM reflectivity models: velocity perturbation related reflectivity model and normal-incidence reflection coefficient related reflectivity model. Each has its specific physical meaning and provides different inverted results. In this paper, we first give a brief review about the two different definitions. Then, we compare the differences of these two methods and build a mathematical relationship. In the definition related to reflection coefficient model, we rescale the defined reflectivity with background velocity. Also, in source wavefield reconstruction, we use an effective trick by moving file pointer to fetch data from disk to reduce the memory cost. Finally, we test these two LSRTM schemes using the Marmousi model. We observe that the two inverted reflectivities are different, although they both image the subsurface discontinuities well. We furthermore extract traces from the inversion results and compare them with the true reflectivity models, respectively, to verify the physical definitions of them. [ABSTRACT FROM AUTHOR] more...

In this paper, we present and evaluate a novel multilevel hybrid-chaotic oscillator. The proposed generalized multilevel-hybrid chaotic oscillator (GM-HCO) was created by combining a multilevel discrete function generated from user data with a continuous function having a damping factor greater than ln(2) to achieve variable rates and adaptive carrier frequencies. Improved spectral efficiency and lower complexity of the transceiver compared with differentially coherent systems were achieved by multilevel signals at the transmitter and a matched filter at the receiver. An exact analytical solution for the generalized fixed basis function and the impulse response of the matched filter were also derived. The bit error rate (BER) expression of the GM-HCO was derived for two levels. It was found that the noise performance of the proposed system was better than a hybrid chaotic system based on forward time and differential chaos shift keying (DCSK). A comprehensive set of simulations were carried out to evaluate the performance of the proposed system with chaotic communication systems in the presence of additive white Gaussian noise (AWGN). The performance of the proposed system was comparable with that of conventional communication systems. The results demonstrate that the proposed system can offer better noise performance than existing chaotic communication systems, and it also offers variable transmitter frequencies and improved spectral efficiency. Noise-like behavior of the chaotic signals provides an additional layer of security at the physical layer compared with conventional (sinusoidal) communication systems. [ABSTRACT FROM AUTHOR] more...

ABSTRACT Numerical implementation of the gradient of the cost function in a gradient-based full- waveform inversion (FWI) is essentially a migration operator used in wave equation migration. In FWI, minimizing different data residual norms results in different weighting strategies of data residuals at receiver locations prior to back-propagation into the medium. In this paper, we propose different scaling methods to the receiver wavefield and compare their performances. Using time-domain reverse-time migration (RTM), we show that compared to conventional algorithms, this type of scaling is able to significantly suppress non-Gaussian noise, i.e., outliers. Our tests also show that scaling by its absolute norm produces better results than other approaches. [ABSTRACT FROM AUTHOR] more...

Sengupta (1989) showed that, for the first-come-first-served (FCFS) G/G/I queue, the workload and attained waiting time of a Customer in service have the same stationary distribution. Sakasegawa and Wolff (1990) derived a sample path version of this result, showing that the empirical distribution of the workload values over a busy period of a given sample path is identical to that of the attained waiting time values over the same period. For a given sample path of an FCFS GIG/s queue, we construct a dual sample path of a dual queue which is FCFS G/G/s in reverse time. It is shown that the workload process on the original sample path is identical to the total attained waiting time process on the dual sample path. As an application of this duality relation, we show that, for a time-stationary FCFS M/M/s/k queue, the workload process is equal in distribution to the time-reversed total attained waiting time process. [ABSTRACT FROM AUTHOR] more...

The Fire and Fire Surrogate study--a replicated, manipulative experiment--sought the most economically and ecologically efficient way to restore the nation's fire-maintained ecosystems. As part of this study, we conducted a 3-year mark--recapture study, comprising 105,000 trap-nights, to assess demographic responses of cotton mice (Peromyscus gossypinus) to Fire and Fire Surrogate treatments at the Gulf Coastal Plain site, where longleaf pine was the ecosystem to be restored. We compared competing models to evaluate restoration effects on variation in apparent survival and recruitment over time, space, and treatment, and incorporated measures of available source habitat for cotton mice with reverse-time modeling to infer immigration from outside the study area. The top-ranked survival model contained only variation over time, but the closely ranked 2nd and 3rd models included variation over space and treatment, respectively. The top 4 recruitment models all included effects for availability of source habitat and treatments. Burning appeared to degrade habitat quality for cotton mice, showing demographic characteristics of a sink, but treatments combining fire with thinning of trees or application of herbicide to the understory appeared to improve habitat quality, possibly creating sources. Bottomland hardwoods outside the study also acted as sources by providing immigrants to experimental units. Models suggested that population dynamics operated over multiple spatial scales. Treatments applied to 15-ha stands probably only caused local variation in vital rates within the larger population. [ABSTRACT FROM AUTHOR] more...

The features of processes of chaotic discrete map in reverse time are considered. The fractal distribution of reverse iteration points is indicated. The approach to investigating reverse points manifold based on special ordering methods is proposed. [ABSTRACT FROM AUTHOR] more...