Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications
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 indepen...
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doaj-16b3aa533c954d9e9ca7dc5e5e6396f82020-11-24T22:09:45ZengMDPI AGEntropy1099-43002018-01-012016310.3390/e20010063e20010063Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their ApplicationsXiao-Li Ding0Juan J. Nieto1Department of Mathematics, Xi’an Polytechnic University, Xi’an 710048, ChinaDepartamento de Estatística, Análisis Matemático y Optimización, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, SpainIn 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.http://www.mdpi.com/1099-4300/20/1/63multi-time scale fractional stochastic differential equationsfractional Brownian motionfractional stochastic partial differential equationanalytical solution |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Xiao-Li Ding Juan J. Nieto |
spellingShingle |
Xiao-Li Ding Juan J. Nieto Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications Entropy multi-time scale fractional stochastic differential equations fractional Brownian motion fractional stochastic partial differential equation analytical solution |
author_facet |
Xiao-Li Ding Juan J. Nieto |
author_sort |
Xiao-Li Ding |
title |
Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications |
title_short |
Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications |
title_full |
Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications |
title_fullStr |
Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications |
title_full_unstemmed |
Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications |
title_sort |
analytical solutions for multi-time scale fractional stochastic differential equations driven by fractional brownian motion and their applications |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2018-01-01 |
description |
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. |
topic |
multi-time scale fractional stochastic differential equations fractional Brownian motion fractional stochastic partial differential equation analytical solution |
url |
http://www.mdpi.com/1099-4300/20/1/63 |
work_keys_str_mv |
AT xiaoliding analyticalsolutionsformultitimescalefractionalstochasticdifferentialequationsdrivenbyfractionalbrownianmotionandtheirapplications AT juanjnieto analyticalsolutionsformultitimescalefractionalstochasticdifferentialequationsdrivenbyfractionalbrownianmotionandtheirapplications |
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1725810902213591040 |