We derive the strong consistency
of the least squares estimator for the drift coefficient of a fractional
stochastic differential system. The drift coefficient is one-sided
dissipative Lipschitz and the driving noise is additive 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 least squares estimator. This is from some joint work with David Nualart
and Hongjuan Zhou. |