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.
About the Authors
Maxim M. Vaskouski
Belarusian State University
Belarus
Belarus
Vaskouski Maxim Mikhailovich – Ph. D. (Physics and Mathematics), Associate professor
4, Nezavisimosti Ave., 220030, Minsk
Ilya V. Kachan
Belarusian State University
Belarus
Belarus
Kachan Ilya Vadimovich – Undergraduate, Assistant of the Department
4, Nezavisimosti Ave., 220030, Minsk
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