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Stochastic differential equations with variable structure driven by multiplicative Gaussian noise and sliding mode dynamic (1504.06439v1)
Published 24 Apr 2015 in math.OC
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.