On reflected Stratonovich stochastic differential equations

TL;DR

This paper investigates the existence, uniqueness, and approximation of solutions to reflected Stratonovich stochastic differential equations driven by jump processes, extending Wong-Zakai approximation results.

Contribution

It introduces new results on the well-posedness and approximation of reflected Stratonovich SDEs with jumps, generalizing previous Wong-Zakai approximation findings.

Findings

Established existence and uniqueness of solutions.

Extended Wong-Zakai approximation results.

Provided methods for approximating solutions with jumps.

Abstract

We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we generalize known results on the Wong-Zakai type approximations.