On Function of Evolution of Distribution for Time Homogeneous Markov Processes
Abstract
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one dimensional distributions of a process is introduced. This, along with the notion of bridge operators which determine the backward structure, as opposed to the forward structure determined by the usual semi-group operators, paves a way to the new approach for dealing with finite-dimensional distributions of Markov processes. This, in particular, produces explicit formulas which effectively simplify the computations of finite-dimensional distributions, giving an alternative to the standard approach based on computations using the chain rule of transition densities. Various examples illustrating the new approach are presented.
Cite
@article{arxiv.2206.09451,
title = {On Function of Evolution of Distribution for Time Homogeneous Markov Processes},
author = {Tomasz Bielecki and Jacek Jakubowski and Maciej Wiśniewolski},
journal= {arXiv preprint arXiv:2206.09451},
year = {2022}
}