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Filippov’s theorem for stochastic differential inclusions driven by semimartingales and applications

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  • Michta, Mariusz

Abstract

In this work, we present a stochastic version of Filippov’s theorem and its application to the qualitative analysis of stochastic differential inclusions with respect to semimartingale integrators. Based on this result, we establish, in particular, the Lipschitz dependence of the solution set of the considered inclusion on the initial sets, as well as its continuous dependence on the multivalued operators and the integrators involved. Finally, we provide analogous continuity properties for the attainable sets generated by the solutions to the given inclusion. Additionally, we present several remarks containing comments on possible extensions and examples illustrating the application of Filippov’s Theorem. The results obtained in this paper extend the applicability of Filippov’s theorem in the stochastic setting.

Suggested Citation

  • Michta, Mariusz, 2026. "Filippov’s theorem for stochastic differential inclusions driven by semimartingales and applications," Stochastic Processes and their Applications, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:spapps:v:201:y:2026:i:c:s0304414926001973
    DOI: 10.1016/j.spa.2026.105065
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