一类随机微分变分不等式

A Class of Stochastic Differential Variational Inequalities

在一定条件下证明随机微分变分不等式解的存在性与唯一性.首先,证明随机微分变分不等式等价于随机投影系统;其次,用压缩映射原理证明该系统的解的存在性与唯一性;最后,考虑含参的随机微分变分不等式,并证明在一定条件下其解的稳定性.

In this paper,we introduce a stochastic differential variational inequality,and find the unique adapted solution of the stochastic differential variational inequality under some suitable conditions.First,we prove that the stochastic differential variational inequality is equivalent to a stochastic project system.Then,we find the unique adapted solution of the stochastic differential variational inequality by using the contraction mapping principle.Finally,we consider a stochastic differential variational inequality with parameters,and prove its adapted solution is continuous.