On solutions to set-valued and fuzzy stochastic differential equations

摘要

We study existence and uniqueness of solutions to nonlinear set-valued stochastic differential equations driven by multidimensional Brownian motion. The conditions imposed on the equation's coefficients are non-Lipschitz. The drift coefficient is set-valued and diffusion coefficient is single-valued, both coefficients are random. The approach used in this paper allows the solutions to be set-valued stochastic processes. The set-valued results are then extended for the parallel studies of nonlinear fuzzy stochastic differential equations with solutions being fuzzy stochastic processes. (C) 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.