The Existence And Uniqueness Of The Solutions Of Stochastic Differential Equations With Singular Drift

In the field of stochastic analysis,it is an important subject to study the existence and uniqueness of solutions of stochastic differential equations(SDEs)with singular drift.In general,the solutions of deterministic differential equations with singular drift are not unique and even don’t exist.The existing results show that the solutions of stochastic differential equations with singular drift driven by Brownian motion are unique under extremely weak conditions.In this paper,several classical articles in this field are quoted,and the existence and uniqueness of the solution of stochastic differential equations are summarized.The main content of this academic dissertation is as follows:Chapter 1 briefly introduces the background,history of SDE and structure of this academic dissertation.In Chapter 2,we consider a transformation of the phase space that removes the drift,and introduce the existence and uniqueness of solutions of stochastic differential equations with continuous drift.In Chapter 3,we discuss the existence and uniqueness of strong solutions of stochastic differential equations with Sobolev singular drift and additive noise.In Chapter 4,we give the results of existence and uniqueness of solutions to stochastic differential equations with Sobolev singular drift and multiplicative noise.