Czechoslovak Mathematical Journal, Vol. 67, No. 1, pp. 11-28, 2017


On solutions set of a multivalued stochastic differential equation

Marek T. Malinowski, Ravi P. Agarwal

Received February 5, 2015.  First published February 24, 2017.

Abstract:  We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.
Keywords:  multivalued stochastic differential equation; Covitz-Nadler fixed point theorem; multivalued stochastic process
Classification MSC:  93E03, 93C41, 26E25, 60H05, 60H10, 60H20, 60G20
DOI:  10.21136/CMJ.2017.0072-15


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Affiliations:   Marek T. Malinowski, Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland, e-mail: mmalinowski@pk.edu.pl, malinowskimarek@poczta.fm; Ravi P. Agarwal, Department of Mathematics, Texas A&M University - Kingsville, Rhode Hall, W B Ave, Kingsville, Texas 78363-8202, USA, e-mail: agarwal@tamuk.edu

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