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June  2014, 19(4): 1197-1212. doi: 10.3934/dcdsb.2014.19.1197

## Stochastic averaging principle for dynamical systems with fractional Brownian motion

 1 Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710072, China, China, China, China 2 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616

Received  April 2013 Revised  September 2013 Published  April 2014

Stochastic averaging for a class of stochastic differential equations (SDEs) with fractional Brownian motion, of the Hurst parameter $H$ in the interval $(\frac{1}{2},1)$, is investigated. An averaged SDE for the original SDE is proposed, and their solutions are quantitatively compared. It is shown that the solution of the averaged SDE converges to that of the original SDE in the sense of mean square and also in probability. It is further demonstrated that a similar averaging principle holds for SDEs under stochastic integral of pathwise backward and forward types. Two examples are presented and numerical simulations are carried out to illustrate the averaging principle.
Citation: Yong Xu, Rong Guo, Di Liu, Huiqing Zhang, Jinqiao Duan. Stochastic averaging principle for dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1197-1212. doi: 10.3934/dcdsb.2014.19.1197
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