Yaozhong Hu, University of Alberta

Drift Parameter Estimator in Linear and Nonlinear Stochastic Differential Equation Driven by Fractional Brownian Motions

Abstract

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.