Symmetric Fuzzy Stochastic Differential Equations Driven by Fractional Brownian Motion

Abstract

We consider symmetric fuzzy stochastic differential equations where diffusion and drift terms arise in a symmetric way at both sides of the equations and diffusion parts are driven by fractional Brownian motions. Such equations can be used in real-life hybrid systems, which include properties of being both random and fuzzy and reflecting long-range dependence. By imposing on the mappings occurring in the equation the conditions of Lipschitzian continuity and additional constraints by an integrable stochastic process, we construct an approximation sequence of fuzzy stochastic processes and apply this to prove the existence of a unique solution to the studied equation. Finally, a model from population dynamics is considered to illustrate the potential application of our equations.

Keywords

• fuzzy stochastic differential equations
• symmetric fuzzy fractional stochastic differential equations
• fractional Brownian motion
• fuzzy stochastic process
• fuzzy stochastic integral