Wong--Zakai approximation of regime-switching SDEs via rough path theory

Abstract

This paper investigates the convergence of Wong--Zakai approximations to regime-switching stochastic differential equations, generated by a collection of finite-variation approximations to Brownian motion. We extend the results of Nguyen and Peralta (2021) to ${\mathbb{R}}^d$-valued RSSDE by utilising rough path theoretic tools, acquiring the same modification of rate.

22 pages, 1 figure