Markov Chain Approximations to Singular Stable-like Processes

TL;DR

This paper develops Markov chain approximations for singular stable-like processes, establishing properties of the chains, constructing approximations, and identifying conditions for their convergence to the target processes.

Contribution

It introduces a framework for approximating singular stable-like processes with Markov chains and provides necessary conditions for their weak convergence.

Findings

Established properties of certain Markov chains.

Constructed Markov chain approximations for singular stable-like processes.

Derived necessary conditions for weak convergence.

Abstract

We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these chains to singular stable-like processes.