Fuzzy stochastic differential equations driven by fractional Brownian motion

Abstract

Abstract In this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an approximation method to the fractional stochastic integral to study the existence and uniqueness of the solutions. As an example, in financial models, we obtain the solution for an equation with linear coefficients.

Keywords

• Fuzzy set theory
• Fuzzy stochastic processes
• Fuzzy stochastic differential equation
• Fractional Brownian motion