Fluid Limits of Pure Jump Markov Processes: a Practical Guide

TL;DR

This paper provides a simplified guide to understanding how rescaled pure jump Markov processes converge to solutions of differential equations, facilitating modeling of large complex systems.

Contribution

It offers a clearer, more accessible presentation of fluid limit results for pure jump Markov processes, aiding practical modeling efforts.

Findings

Rescaled Markov chains converge uniformly to differential equation solutions

Simplified presentation compared to existing literature

Applicable to modeling large random systems

Abstract

A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be used to build parsimonious models of large random or pseudo-random systems.