Least Squares Estimator for Vasicek Model Driven by Sub-fractional Brownian Processes from Discrete Observations

TL;DR

This paper develops and analyzes least squares estimators for the Vasicek model driven by sub-fractional Brownian motion, focusing on parameter estimation from discrete data, their consistency, distribution, and validation through simulations.

Contribution

It introduces a novel least squares estimation approach for the Vasicek model driven by sub-fractional Brownian motion and studies its theoretical properties and practical validation.

Findings

Estimators are strongly consistent.

Asymptotic normality of estimators is established.

Numerical simulations validate the estimators' effectiveness.

Abstract

We study the parameter estimation problem of Vasicek Model driven by sub-fractional Brownian processes from discrete observations, and let {S_t^H,t>=0} denote a sub-fractional Brownian motion whose Hurst parameter 1/2<H<1 . The studies are as follows: firstly, two unknown parameters in the model are estimated by the least squares method. Secondly, the strong consistency and the asymptotic distribution of the estimators are studied respectively. Finally, our estimators are validated by numerical simulation.