Stochastic inclusions with non-continuous set-valued operators

Mariusz Michta

doi:10.3934/proc.2009.2009.548

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2009, Volume 2009: 548-557. Doi: 10.3934/proc.2009.2009.548 open access

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Stochastic inclusions with non-continuous set-valued operators

Mariusz Michta^1,

1.
Faculty of Mathematics, Computer Sciences and Ekonometrics, University of Zielona Góra, Szafrana 4a,, 65-516 Zielona Góra

Received: July 2008

Revised: March 2009

Published: August 2009

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Abstract

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.

Keywords:

Stochastic inclusion,
upper lower solution,
increasing and upper separated multifunctions.

Mathematics Subject Classification: Primary 60H20, 90B05; Secondary 90C30.

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