The interrelation between stochastic differential inclusions and set-valued stochastic differential equations
作者: Marek T. MalinowskiMariusz Michta
作者单位: 1Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra, Poland
2Institute of Mathematics and Informatics, Opole University, Oleska 48, 45-052 Opole, Poland
刊名: Journal of Mathematical Analysis and Applications, 2013, Vol.408 (2), pp.733-743
来源数据库: Elsevier Journal
DOI: 10.1016/j.jmaa.2013.06.055
关键词: Stochastic differential inclusionSet-valued stochastic differential equationSet-valued stochastic integral equation
英文摘要: Abstract(#br)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 ‖ ⋅ ‖ L 2 -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...
全文获取路径: Elsevier  (合作)
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