Stochastic differential equations with variable structure driven by multiplicative Gaussian noise and sliding mode dynamic

TL;DR

This paper investigates the existence of weak solutions for stochastic differential equations with variable structure and sliding mode control driven by multiplicative Gaussian noise, including systems with jumps and nonlinearities.

Contribution

It provides new existence results for weak solutions of discontinuous stochastic differential equations with variable structure and sliding mode dynamics under multiplicative Gaussian noise.

Findings

Established existence of weak solutions for finite-dimensional systems.

Extended results to stochastic diffusion equations with multiplicative noise.

Addressed equations with jump nonlinearities and discontinuities.

Abstract

This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with variable structure, that is with jump nonlin- earity. The treatment covers the finite dimensional stochastic systems and the stochastic diffusion equation with multiplicative noise.