Set-valued stochastic differential equation in M-type 2 Banach space | Zendy

Itaru Mitoma | Zendy; Yoshiaki Okazaki | Zendy; Jinping Zhang | Zendy

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Set-valued stochastic differential equation in M-type 2 Banach space

Author(s) -

Itaru Mitoma,

Yoshiaki Okazaki,

Jinping Zhang

Publication year - 2010

Publication title -

communications on stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.224

H-Index - 10

eISSN - 2688-6669

pISSN - 0973-9599

DOI - 10.31390/cosa.4.2.06

Subject(s) - mathematics , banach space , type (biology) , stochastic differential equation , c0 semigroup , set (abstract data type) , infinite dimensional vector function , space (punctuation) , mathematical analysis , pure mathematics , banach manifold , lp space , computer science , ecology , biology , programming language , operating system

Let (›,F,{Ft},P) be a complete probability space with filtra- tion {Ft}, (X ,H,µ) an abstract Wiener space of M-type 2, and {Bt : t ‚ 0} an X -valued Brownian motion such that the distribution of the random func- tion ti1/2Bt : › ! X is µ for any t > 0. We consider the strong solutions to a set-valued stochastic dierential equation with a set-valued drift and a single valued diusion driven by dBt. Under some suitable conditions, the existence and uniqueness of strong solutions are obtained.

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