Least squares estimators for discretely observed stochastic processes driven by small fractional noise

TL;DR

This paper investigates the properties of least squares estimators for stochastic differential equations driven by small fractional noise, establishing their consistency and convergence rates as noise diminishes and sample size grows.

Contribution

It provides new theoretical results on the strong consistency and convergence rates of LSE for SDEs with fractional noise under small dispersion conditions.

Findings

LSE is strongly consistent as noise diminishes.

Convergence rate of the estimator is established.

Results apply when the dispersion coefficient approaches zero.

Abstract

We study the problem of parameter estimation for discretely observed stochastic differential equations driven by small fractional noise. Under some conditions, we obtain strong consistency and rate of convergence of the least square estimator(LSE) when small dispersion coefficient converges to 0 and sample size converges to infty.