On solutions to set-valued and fuzzy stochastic differential equations

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.