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Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
Yong Xu,
Bin Pei,
Jiang-lun Wu 
Stochastics and Dynamics, Start page: 1750013
Swansea University Author:
Jiang-lun Wu
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DOI (Published version): 10.1142/S0219493717500137
Abstract
In this paper, we are concerned with the stochastic averaging principle for stochastic differential equations (SDEs) with non-Lipschitz coefficients driven by fractional Brownian motion (fBm) of the Hurst parameter H ∈ ( 1 , 1). We define the stochastic integrals with respect to the fBm in the integ...
| Published in: | Stochastics and Dynamics |
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| ISSN: | 1793-6799 |
| Published: |
2017
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa28501 |
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| Abstract: |
In this paper, we are concerned with the stochastic averaging principle for stochastic differential equations (SDEs) with non-Lipschitz coefficients driven by fractional Brownian motion (fBm) of the Hurst parameter H ∈ ( 1 , 1). We define the stochastic integrals with respect to the fBm in the integral formulation of the SDEs as pathwise integrals and we adopt the non-Lipschitz condition proposed by Taniguchi (1992) which is a much weaker condition with wider range of applications. The averaged SDEs are established. We then use their corresponding solutions to approximate the solutions of the original SDEs both in the sense of mean square and of probability. One can find that the similar asymptotic results are suitable for those non-Lipschitz SDEs with fBm under different types of stochastic integrals. |
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| Keywords: |
Stochastic differential equations; non-Lipschitz coefficients; fractional Brow- nian motion; stochastic averaging; pathwise integrals. |
| College: |
Faculty of Science and Engineering |
| Start Page: |
1750013 |