Ding Xiao-Li, Nieto Juan J
Department of Mathematics, Xi'an Polytechnic University, Xi'an 710048, China.
Departamento de Estatística, Análisis Matemático y Optimización, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain.
Entropy (Basel). 2018 Jan 16;20(1):63. doi: 10.3390/e20010063.
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.
在本文中，我们研究由分数布朗运动驱动的多时间尺度分数阶随机微分方程的解析解。我们首先将由分数布朗运动驱动的齐次多时间尺度分数阶随机微分方程分解为独立的微分子方程，并给出它们的解析解。然后，我们利用常数变易法得到由分数布朗运动驱动的非齐次多时间尺度分数阶随机微分方程的解。最后，我们给出三个例子来说明我们所得结果的适用性。
