Existence and convergence for stochastic differential variational inequalities

Year 2023, Volume: 52 Issue: 6 - Special Issue: Nonlinear Evolution Problems with Applications, 1461 - 1479, 03.11.2023

Fei Guan , Van Thien Nguyen , Zijia Peng

https://doi.org/10.15672/hujms.1141495

Abstract

In this paper, we consider a class of stochastic differential variational inequalities (for short, SDVIs) consisting of an ordinary differential equation and a stochastic variational inequality. The existence of solutions to SDVIs is established under the assumption that the leading operator in the stochastic variational inequality is $P$-function and $P_{0}$-function, respectively. Then, by using the sample average approximation and time stepping methods, two approximated problems corresponding to SDVIs are introduced and convergence results are obtained.

Keywords

Stochastic differential variational inequality, P-function, convergence, P_0-function

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