Fuzzy stochastic differential equations driven by fractional Brownian motion
Hossein Jafari, Marek T. Malinowski, M. J. Ebadi
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.
Topics & Concepts
Fractional Brownian motionMathematicsStochastic differential equationUniquenessStochastic partial differential equationRandomnessGeometric Brownian motionBrownian motionPartial differential equationMathematical analysisApplied mathematicsOrdinary differential equationDiffusion processDifferential equationInnovation diffusionComputer scienceStatisticsKnowledge managementFuzzy Systems and OptimizationFractional Differential Equations SolutionsNonlinear Differential Equations Analysis