The interrelation between stochastic differential inclusions and set-valued stochastic differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:408

Article

Malinowski, Marek T.¹  Michta, Mariusz^1,2 

[1] Univ Zielona Gora, Fac Math Comp Sci & Econometr, PL-65516 Zielona Gora, Poland

[2] Opole Univ, Inst Math & Informat, PL-45052 Opole, Poland

关键词: Stochastic differential inclusion;    Set-valued stochastic differential equation;    Set-valued stochastic integral equation;   

DOI  :  10.1016/j.jmaa.2013.06.055

来源: Elsevier

【 摘 要 】

In this paper we connect the well established theory of stochastic differential inclusions with a new theory of set-valued stochastic differential equations. Solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty, bounded, convex and closed subsets of the space L-2 consisting of square integrable random vectors. We show that for the solution X to a set-valued stochastic differential equation corresponding to a stochastic differential inclusion, there exists a solution x for this inclusion that is a parallel to center dot parallel to(L2)-continuous selection of X. This result enables us to draw inferences about the reachable sets of solutions for stochastic differential inclusions, as well as to consider the viability problem for stochastic differential inclusions. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free