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arXiv · 2212.08366

Stochastic differential variational inequalities with applications

Yao-Jia Zhang·Tao Chen·Nan-jing Huang·Xue-song Li
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Abstract

In this paper, we introduce and study a stochastic differential variational inequality (SDVI) which consists of a stochastic differential equation and a stochastic variational inequality. We obtain the existence and uniqueness of the solutions for SDVI by using the iteration method and Gronwall's inequality. Moreover, we show the convergence of Euler scheme for solving SDVI under some mild conditions. Finally, we apply the obtained results to solve the electrical circuits with diodes and the collapse of the bridge problems in stochastic environment.

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Yao-Jia Zhang, Tao Chen, Nan-jing Huang, Xue-song Li. 2022-12-16. Stochastic differential variational inequalities with applications. https://arxiv.org/abs/2212.08366

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