Special Session 37: Recent development of stochastic optimal control, applications and deep learning methods

Filippov`s Theorem for stochastic differential inclusions driven by semimartingales
Mariusz Michta
Institute of Mathematics, University of Zielona Gora
Poland
Co-Author(s):    Mariusz Michta
Abstract:
In the talk, we present a stochastic version of Filippov's Theorem and its application to the qualitative analysis of stochastic differntial inclusions with respect to semimartingale integrators. Based on this result, in particular, we establish the Lipschitz dependence of the solution set of the considered inclusion on initial sets, and continuous dependence on the multivalued operators and the integrators involved. We also provide analogous continuity properties for the attainable sets generated by the solutions of the given inclusion.