Asymptotic Expansion for Distribution of Markovian Random Motion

TL;DR

This paper develops an asymptotic expansion method for analyzing the distribution of particles undergoing Markovian random motion, simplifying complex equations into more manageable forms for better understanding.

Contribution

It introduces a novel asymptotic expansion approach that reduces singularly perturbed equations to regular ones in the context of Markovian random motion.

Findings

Derived asymptotic expansion formulas for particle distribution

Reduced complex equations to simpler forms for analysis

Enhanced understanding of diffusion approximation in Markov processes

Abstract

In this paper we study an asymptotic expansion for the distribution of a random motion of a particle driven by a Markov process in diffusion approximation. We show that the singularly perturbed equation of a Markovian random motion can be reduced to the regularly perturbed equation for the distribution of the random motion.