A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise

Abstract

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter H>1/2. The estimator is based on discrete time observations of the stochastic differential equation, and using tools from ergodic theory and stochastic analysis we derive its strong consistency.