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ASYMPTOTIC EXPANSIONS OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY MULTIVARIATE FRACTIONAL BROWNIAN MOTIONS

https://doi.org/10.29235/1561-8323-2018-62-4-398-405

Abstract

In this article, n-dimensional stochastic differential equations driven by multivariate fractional Brownian motions with the Hurst indices greater than 1/3 and a drift term are considered. We have obtained an expansion of expectations Ptg (x) = Eg (Xxt) for small t, where Xxt denotes the solution of the mentioned equation with an initial value x, and g: Rn → R is a sufficiently smooth function.

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ISSN 1561-8323 (Print)
ISSN 2524-2431 (Online)