Boundedness and continuity of solutions for stochastic differential inclusions on infinite dimensional space
Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 807-816
Published online December 1, 2007
Yong Sik Yun and Sang Uk Ryu
Cheju National University, Cheju National University
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
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