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The boundedness of solutions for stochastic differential inclusions

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Abstract

We consider the stochastic differential inclusion of theform dX_tin sigma(t,X_t)dB_t+b(t,X_t)dt, where sigma, b areset-valued maps, B is a standard Brownian motion. We prove theboundedness of solutions under the assumption that sigma andb satisfy the local Lipschitz property and linear growth.

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