Approximation solution of backward doubly fuzzy stochastic differential equations

Abstract

In this paper, we propose a new formula for the backward doubly fuzzy stochastic differential equations (BFDSDEs), In the beginning, we present some basic concepts, definitions, and Hypotheses to obtain the numerical scheme for BFDSDEs, as our scheme depends on the partition of interval [0, T]. In our work, we prove that under Lipschitz conditions, the approximation solution for the backward fuzzy doubly stochastic differential equations converges to the exact solution by using mean square error, and prove the existence and uniqueness of approximations solutions to BFDSDEs.