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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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.

Article information

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

Dates
First available in Project Euclid: 16 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1255700202

Digital Object Identifier
doi:10.2748/tmj/1255700202

Mathematical Reviews number (MathSciNet)
MR2568262

Zentralblatt MATH identifier
1198.60027

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.tmj/1255700202


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