Local limit theorem for time-inhomogeneous functions of Markov processes

TL;DR

This paper establishes a local limit theorem for integrals of time-inhomogeneous functions of continuous-time Markov processes, with applications to analyzing fast-oscillating perturbations in linear dynamical systems.

Contribution

It introduces a local limit theorem for time-inhomogeneous functions of Markov processes, extending classical results to non-stationary settings.

Findings

Proves a local limit theorem for continuous-time Markov processes.

Applies the theorem to fast-oscillating perturbations in linear systems.

Provides a framework for analyzing non-stationary stochastic processes.

Abstract

In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in the study of the fast-oscillating perturbations of linear dynamical systems.