Existence And Convergence Of Solution For Two Kinds Of Stochastic Differential Variational Inequalities

The differential variational inequality（for short,DVI）,initially introduced by Aubin and Cellina in 1984 and systematically examined by Pang and Stewart in 2008,is the source of problem in this paper.DVI has been pointed out to be a powerful mathematical tool to represent models involving both dynamics and constraints in the form of inequalities.In chapter 1,we introduce the research background and current situation of stochastic differential variational inequalities.In chapter 2,we give the symbols and definitions,lemmas and other relevant knowledge throughout the whole text.In chapter 3,we consider a class of stochastic differential variational inequalities consist-ing of an ordinary differential equation and a stochastic variational inequality.The existence of solutions to stochastic differential variational inequalities is established under the assumption that the leading operator in the stochastic variational inequality is P-function and P₀-function,respectively.Then,using the theorem of large numbers get the sample average approximation and time stepping methods,two approximated problems corresponding to stochastic differen-tial variational inequalities are introduced and convergence results are obtained.In chapter 4,we consider a class of stochastic differential variational inequalities（for short,SDVIs）consisting of a stochastic ordinary differential equation and a stochastic vari-ational inequality.The existence of solutions to SDVIs is proved under two cases that the leading operator in the stochastic variational inequality is P-function and P₀-function.Then,the least-norm solution to the second case is obtained by a regularized method.Moreover,the mean square convergence and error bounds of the time-stepping method to SDVIs are established.In chapter 5,we summarize the research issues and give the next research prospects.