Tohoku Mathematical Journal

On the solutions of set-valued Stochastic differential equations in M-type 2 Banach spaces

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

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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.

Article information

Tohoku Math. J. (2), Volume 61, Number 3 (2009), 417-440.

First available in Project Euclid: 16 October 2009

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Zentralblatt MATH identifier

Primary: 65C30: Stochastic differential and integral equations
Secondary: 26E25: Set-valued functions [See also 28B20, 49J53, 54C60] {For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx} 54C65: Selections [See also 28B20]

M-type 2 Banach space integrals of set-valued stochastic processes set-valued stochastic differential equation


Zhang, Jinping; Li, Shoumei; Mitoma, Itaru; Okazaki, Yoshiaki. On the solutions of set-valued Stochastic differential equations in M-type 2 Banach spaces. Tohoku Math. J. (2) 61 (2009), no. 3, 417--440. doi:10.2748/tmj/1255700202.

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