Drift parameter estimation for nonlinear stochastic differential equations driven by fractional Brownian motion

We derive the strong consistency of the least squares estimator (LSE) for the drift coefficient of a fractional stochastic differential system. The drift coefficient is one-sided dissipative Lipschitz and the driving noise is additive and fractional with Hurst parameter H∈(14,1). We assume that continuous observation is possible. The main tools are ergodic theorem and Malliavin calculus. As a by-product, we derive a maximum inequality for Skorohod integrals, which plays an important role to obtain the strong consistency of the LSE.