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

TL;DR

This paper proposes a least squares estimator for parameters in stochastic differential equations driven by fractional noise, demonstrating its strong consistency through ergodic and stochastic analysis tools.

Contribution

It introduces a novel least squares-type estimator for SDEs with fractional noise and proves its strong consistency based on discrete observations.

Findings

Estimator is strongly consistent.

Applicable to SDEs with Hurst parameter H>1/2.

Utilizes ergodic theory and stochastic analysis techniques.

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.