Asymptotic properties of parameter estimators in Vasicek model driven by tempered fractional Brownian motion

TL;DR

This paper analyzes the asymptotic behavior of least-squares estimators for the drift parameters in a Vasicek model driven by tempered fractional Brownian motion, extending previous work on estimator properties.

Contribution

It derives the asymptotic distributions of the estimators, advancing understanding of their long-term statistical properties in this specific stochastic setting.

Findings

Derived the asymptotic distributions of estimators

Extended previous work on estimator consistency

Provided theoretical insights into parameter estimation in complex stochastic models

Abstract

The paper focuses on the Vasicek model driven by a tempered fractional Brownian motion. We derive the asymptotic distributions of the least-squares estimators (based on continuous-time observations) for the unknown drift parameters. This work continues the investigation by Mishura and Ralchenko (Fractal and Fractional, 8(2:79), 2024), where these estimators were introduced and their strong consistency was proved.