Carr-Nadtochiy's Weak Reflection Principle for Markov Chains on $\mathbf{Z}^d$

TL;DR

This paper extends Carr and Nadtochiy's weak reflection principle from 1-dimensional diffusions to Markov chains on multi-dimensional integer lattices, providing a discrete analogue.

Contribution

It introduces a discrete version of the weak reflection principle applicable to Markov chains on  integer lattices, generalizing previous diffusion-based results.

Findings

Established a discrete weak reflection principle for  Markov chains

Extended continuous diffusion results to discrete lattice settings

Provided theoretical framework for future applications in stochastic processes

Abstract

The present paper establishes a discrete version of the result obtained by P. Carr and S. Nadtochiy (2011) for 1-dimensional diffusion processes. Our result is for Markov chains on $\mathbf{Z}^d$.