相关论文: Spectral methods for bivariate Markov processes wi…

We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $\xi$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $\xi$. Our…

The notion of Markov duality between two Markov processes that can live in two different configurations spaces $(x,{\tilde x})$ is revisited via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right…

In an infinitesimal probability space we consider operators which are infinitesimally free and one of which is infinitesimal, in that all its moments vanish. Many previously analysed random matrix models are captured by this framework. We…

We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…

When modeling propagation and scattering phenomena using integral equations discretized by the boundary element method, it is common practice to approximate the boundary of the scatterer with a mesh comprising elements of size approximately…

We construct and analyze the Jacobi process - in mathematical biology referred to as Wright-Fisher diffusion - using a Dirichlet form. The corresponding Dirichlet space takes the form of a Sobolev space with different weights for the…

We review the concepts of the index of a Fredholm operator, the spectral flow of a curve of self-adjoint Fredholm operators, the Maslov index of a curve of Lagrangian subspaces in symplectic Hilbert space, and the eta invariant of operators…

We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…

We develop a spectrally accurate numerical method to compute solutions of a model partial differential equation used in plasma physics to describe diffusion in velocity space due to Fokker-Planck collisions. The solution is represented as a…

We study the numerical differentiation formulae for functions given in grids with arbitrary number of nodes. We investigate the case of the infinite number of points in the formulae for the calculation of the first and the second…

This paper presents a stochastic approach to theorems concerning the behavior of iterations of the Bernstein operator $B_n$ taking a continuous function $f \in C[0,1]$ to a degree-$n$ polynomial when the number of iterations $k$ tends to…

We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with…

A possibility to use an integral operator for establishing the link between physical and structural levels of materials in modeling diffusion processes is considered. We show how to perform the transition from the stochastic description of…

Known results on the moments of the distribution generated by the two-locus Wright-Fisher diffusion model and a duality between the diffusion process and the ancestral process with recombination are briefly summarized. A numerical methods…

In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more…

We study the spectra for a class of differential operators with asymptotically constant coefficients.These operators widely arise as the linearizations of nonlinear partial differential equations about patterns or nonlinear waves. We…

In this paper we propose a Monte Carlo maximum likelihood estimation strategy for discretely observed Wright-Fisher diffusions. Our approach provides an unbiased estimator of the likelihood function and is based on exact simulation…

We study a class of Markov processes with finite state space and continuous time that have product form stationary distributions. We obtain a number of examples that can generate conjectures for diffusions with inert drift.

In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation…