Tohoku Mathematical Journal
2009
September
SECOND SERIES VOL. 61, NO. 3

Tohoku Math. J.
61 (2009), 417-440

Title ON THE SOLUTIONS OF SET-VALUED STOCHASTIC DIFFERENTIAL EQUATIONS IN M-TYPE 2 BANACH SPACES

Author Jinping Zhang, Shoumei Li, Itaru Mitoma and Yoshiaki Okazaki

(Received July 24, 2008, revised April 28, 2009)
Abstract. In a certain Banach space called an M-type 2 Banach space (including Hilbert spaces), we consider a set-valued stochastic differential equation with a set-valued drift term and a single valued diffusion term, under the Lipschitz continuity conditions, and we prove the existence and uniqueness of strong solutions which are continuous in the Hausdorff distance.

2000 Mathematics Subject Classification. Primary 65C30; Secondary 26E25, 54C65.
Key words and phrases. M-type 2 Banach space, integrals of set-valued stochastic processes, set-valued stochastic differential equation.

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