Fuzzy set-valued Lebesgue integral and fuzzy stochastic differential equation

Abstract

In this paper, we firstly recall some basic results about set-valued and fuzzy set-valued stochastic processes. Secondly, we shall discuss the Lebesgue integral of a fuzzy set-valued stochastic process with respect to time t, especially the Lebesgue integral is a fuzzy set-valued stochastic process. Finally we prove a theorem of existence and uniqueness of solution of fuzzy set-valued stochastic differential equation.