Stochastic inclusions with non-continuous set-valued operators
Mariusz Michta - Faculty of Mathematics, Computer Sciences and Ekonometrics, University of Zielona Góra, Szafrana 4a,, 65-516 Zielona Góra, Poland (email)
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
Received: July 2008; Revised: March 2009; Published: September 2009.