Boundedness and continuity of solutions for stochastic differential inclusions on infinite dimensional space

Yong Sik Yun; Sang Uk Ryu

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2007; 44(4): 807-816

Printed December 1, 2007

Boundedness and continuity of solutions for stochastic differential inclusions on infinite dimensional space

Yong Sik Yun and Sang Uk Ryu

Cheju National University, Cheju National University

Abstract

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Abstract

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t\in \sigma(X_t)dW_t + b(X_t)dt,$ where $\sigma, b$ are set-valued maps, $W$ is an infinite dimensional Hilbert space valued $Q$-Wiener process, we prove the boundedness and continuity of solutions under the assumption that $\sigma$ and $b$ are closed convex set-valued satisfying the Lipschitz property using approximation.

Keywords: stochastic differential inclusion, Wiener process

MSC numbers: 60D05