Fuzzy stochastic differential equations driven by fractional Brownian motion

Advances in Difference Equations

article

Jafari, Hossein¹  Malinowski, Marek T.²  Ebadi, M. J.¹ 

[1] Department of Mathematics, Chabahar Maritime University;Department of Applied Mathematics, Cracow University of Technology

关键词: Fuzzy set theory;    Fuzzy stochastic processes;    Fuzzy stochastic differential equation;    Fractional Brownian motion;   

DOI  :  10.1186/s13662-020-03181-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY