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Stochastic inclusions with non-continuous set-valued operators

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  • In the paper we consider a stochastic integral inclusion with discontinuous multivalued right hand side, driven by a continuous semimartingale. Using selection properties and lower and upper solutions methods we demonstrate the existence of strong solutions for such inclusions. We extend some recent results both for deterministic differential inclusions and for stochastic differential equations for increasing operators.
    Mathematics Subject Classification: Primary 60H20, 90B05; Secondary 90C30.

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