Markov Chain Approximation of Pure Jump Processes

TL;DR

This paper investigates how continuous-time Markov chains can approximate non-symmetric pure jump processes, using Dirichlet forms and semimartingale techniques, with applications to Markov process approximation.

Contribution

It introduces a new approach to approximate pure jump processes via Markov chains using Dirichlet forms and semimartingale methods.

Findings

Weak convergence established for Markov chain approximations

Method applicable to non-symmetric pure jump processes

Provides a framework for practical Markov process approximation

Abstract

In this paper we discuss weak convergence of continuous-time Markov chains to a non-symmetric pure jump process. We approach this problem using Dirichlet forms as well as semimartingales. As an application, we discuss how to approximate a given Markov process by Markov chains.