Abstract
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
.
Acknowledgement
Authors are grateful to Reviewer for careful reading of the paper and valuable remarks.
Disclosure statement
No potential conflict of interest was reported by the authors.