Reflected stochastic differential equations in a multidimensional non-smooth time-dependent domain

Abstract

This thesis explores the study of asymptotic properties of reflected stochastic differential equations (SDEs), focusing on the study of strong convergence of the Wong-Zakai approximations for reflected SDEs in non-smooth time-dependent domains. Based on the previous article, we first introduced the required assumptions and the test function built for time-dependent domains and the proof. In addition, we also introduced the Skorohod problem to prove the existence and uniqueness of strong solutions to SDEs with reflection. Furthermore, we showed regularity estimation for the Skorohold problem. Moreover, we proved the strong convergence of the Wong-Zakai approximation for SDEs with reflections in non-smooth time-dependent domain. In order to solve the problems caused by constraints on the solution and the appearance of the boundary local time, we showed a specially constructed process associated with the difference of the Wong-Zakai approximations and the solution of the reflected SDEs to control the local time of the boundary.

Date of Award	1 Aug 2024
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Tusheng Zhang (Supervisor) & Denis Denisov (Supervisor)