Differential equations driven by fractional Brownian motion

Abstract

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> 1 2 is proved.It is shown, also, that the solution has finite moments.The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.