Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications
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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
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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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https://doi.org/10.3390/e20010063Sponsors
The work of the Xiao-Li Ding was supported by the Natural Science Foundation of China
(11501436) and Young Talent fund of University Association for Science and Technology in Shaanxi, China (20170701).
The work of Juan J. Nieto has been partially supported by the AEI of Spain under Grant MTM2016-75140-P and co-financed by European Community fund FEDER, and XUNTA de Galicia under grants GRC2015-004 and R2016/022
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c 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)