Brownian motion

Uniqueness

Mathematics

Stochastic differential equation

Knowledge management

Stochastic partial differential equation

Partial differential equation

Geometric Brownian motion

Fractional Brownian motion

Statistics

Randomness

Mathematical analysis

Computer science

Differential equation

Applied mathematics

Innovation diffusion

Ordinary differential equation

Diffusion process

Advances in Difference Equations

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.

Fuzzy stochastic differential equations driven by fractional Brownian motion