Fuzzy and Set-Valued Stochastic Differential Equations with Solutions of Decreasing Fuzziness

Abstract

We consider fuzzy stochastic differential equations in a new formulation. The equations that we examine possess solutions which are the fuzzy stochastic processes with trajectories of decreasing fuzziness in their consecutive values. This is a novelty. We give a theorem that guarantees existence and uniqueness of solutions. Some fuzzy stochastic differential equations are solved explicitly and some visualizations of simulations connected with their solutions are included. All the results can be applied immediately to set-valued stochastic differential equations.