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Entropy 2018, 20(1), 63; https://doi.org/10.3390/e20010063

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

1
Department of Mathematics, Xi’an Polytechnic University, Xi’an 710048, China
2
Departamento de Estatística, Análisis Matemático y Optimización, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain
*
Author to whom correspondence should be addressed.
Received: 21 December 2017 / Revised: 3 January 2018 / Accepted: 11 January 2018 / Published: 16 January 2018
(This article belongs to the Special Issue Entropy in Dynamic Systems)
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Abstract

In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results. View Full-Text
Keywords: multi-time scale fractional stochastic differential equations; fractional Brownian motion; fractional stochastic partial differential equation; analytical solution multi-time scale fractional stochastic differential equations; fractional Brownian motion; fractional stochastic partial differential equation; analytical solution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ding, X.-L.; Nieto, J.J. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications. Entropy 2018, 20, 63.

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