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Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion. (English) Zbl 1433.60040
Summary: In this paper, an averaging principle for multidimensional, time dependent, stochastic differential equations (SDEs) driven by fractional Brownian motion and standard Brownian motion was established. We combined the pathwise approach with the Itô stochastic calculus to handle both types of integrals involved and proved that the original SDEs can be approximated by averaged SDEs in the manner of mean square convergence.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G22 Fractional processes, including fractional Brownian motion
60H05 Stochastic integrals
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