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On multivalued stochastic integral equations driven by a Wiener process in the plane. (English) Zbl 1260.60131

Summary: We define a multivalued stochastic integral in the plane. Then we investigate the multivalued stochastic equation in the plane as an abstract stochastic equation in a hyperspace of subsets of the space of square integrable random vectors. We prove existence and uniqueness of solutions as well as some additional properties. Results similar to a fuzzy-valued stochastic integral equation in the plane are stated as applications.

MSC:

60H20 Stochastic integral equations
60G60 Random fields
26E25 Set-valued functions
34A07 Fuzzy ordinary differential equations
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