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Stochastic differential equations with variable structure driven by multiplicative Gaussian noise and sliding mode dynamic. (English) Zbl 1356.60088

Authors’ abstract: This work is concerned with existence of weak solutions to discontinuous stochastic differential equations driven by multiplicative Gaussian noise and sliding mode control dynamics generated by stochastic differential equations with variable structure, that is with jump non-linearity. The treatment covers the finite dimensional stochastic systems and the stochastic diffusion equation with multiplicative noise.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G15 Gaussian processes
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References:

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