Asymptotic expansions of solutions of stochastic differential equations driven by multivariate fractional Brownian motions having Hurst indices greater than

In this paper, we consider n-dimensional stochastic differential equations driven by multivariate fractional Brownian motion with Hurst indices greater than . Using a Taylor type development we obtain an expansion of expectations for small t, where denotes the solution of the mentioned stochastic differential equation with initial value and is a sufficiently smooth function. Also we compute coefficients appearing in the expansion of in the case when the fractional Brownian motions have the Hurst indices greater than . Finally, we consider the case of commutative vector fields getting Kolmogorov's backward partial differential equation for the function .