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 expectationsPtg (x) = Eg (Xxt)for small t, whereXxtdenotes the solution of the mentioned equation with an initial valuex, andg: Rn→ Ris a sufficiently smooth function.
Highlights
The solution of the mentioned equation with an initial value x, and Keywords: multivariate fractional Brownian motion, rough paths theory, Gubinelli’s derivative, stochastic differential equation, asymptotic expansions
Operators associated with a stochastic differential equation driven by fractional Brownian motions / F
Differential equations driven by fractial Brownian motion / D
Summary
Рассматриваются n-мерные стохастические дифференциальные уравнения с дробными броуновскими движениями, имеющими различные индексы Харста, большие 1/3, и сносом. Для достаточно малых t, где через x t обозначается решение указанного уравнения с начальным значением x, а g. Ключевые слова: дробное броуновское движение, потраекторный интеграл, производная Губинелли, стохастическое дифференциальное уравнение, асимптотическое разложение. М. Асимптотические разложения решений стохастических дифференциальных уравнений с дробными броуновскими движениями / М. ASYMPTOTIC EXPANSIONS OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY MULTIVARIATE FRACTIONAL BROWNIAN MOTIONS
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