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- Title
Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion.
- Authors
Xu, Yong; Pei, Bin; Wu, Jiang-Lun
- 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 . 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.
- Subjects
STOCHASTIC differential equations; AVERAGING method (Differential equations); STOCHASTIC integrals; BROWNIAN motion; LIPSCHITZ spaces
- Publication
Stochastics & Dynamics, 2017, Vol 17, Issue 2, p-1
- ISSN
0219-4937
- Publication type
Article
- DOI
10.1142/S0219493717500137