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On weak solutions to stochastic differential inclusions driven by semimartingales. (English) Zbl 1059.93125

Summary: We consider weak solutions to stochastic inclusions driven by a general semimartingale. We prove the existence of weak solutions and equivalence with the existence of solutions to the martingale problem formulated to such inclusion. Using this, we then analyze the compactness property of the solution set. The presented results extend some of those being known for stochastic differential inclusions of Itô type.

MSC:

93E03 Stochastic systems in control theory (general)
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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