Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2003; 40(1): 159-165

Printed March 1, 2003

Copyright © The Korean Mathematical Society.

The boundedness of solutions for stochastic differential inclusions

Yong Sik Yun

Cheju National University

Abstract

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We consider the stochastic differential inclusion of the form $dX_t\in \sigma(t,X_t)dB_t+b(t,X_t)dt,$ where $\sigma, b$ are set-valued maps, $B$ is a standard Brownian motion. We prove the boundedness of solutions under the assumption that $\sigma$ and $b$ satisfy the local Lipschitz property and linear growth.

Keywords: stochastic differential inclusion, Brownian motion

MSC numbers: 60D05

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