Stochastic Differential Equations With Oblique Reflection On Time-dependent Domains

This thesis is a review.The main content of this thesis is to summarize the previous results and research methods of existence and uniqueness of solutions to stochastic dif-ferential equations with oblique reflection on time-dependent domains.After reading a large related literature,I selected celebrated articles Nystrom?Onskog[19]and Lund-strom?Onskog[17]as the main references.Nystrom?Onskog[19]constructed the right continuous solutions with left limits to Skorohod problem on time-dependent domains through discretization and approximate the time-dependent domains.Subsequently,they used the relevant results of the Skorohod problem on time-dependent domains and the Skorohod representation theorem to construct weak solutions to stochastic differ-ential equations with oblique reflection on time-dependent domains.Lundstrom?On-skog[17]used the constructed test functions and penalty method to prove the existence of solutions to a type of Skorohod problem on time-dependent domains;Then,based on the existence of solutions to Skorohod problem and the estimate of strong solutions to stochastic differential equations with oblique reflection on time-dependent domains,the existence and uniqueness of strong solutions to stochastic differential equations with oblique reflection on time-dependent domains is proved by a Picard iteration scheme.It is hoped that this thesis can provide some references for the researchers who are in-terested in the direction of stochastic differential equations on time-dependent domains.