The Berry-Ess\'{e}en Upper Bounds of Vasicek Model Estimators

TL;DR

This paper derives novel Berry-Esséen upper bounds for estimators in Vasicek models driven by Gaussian processes, extending existing methods to more complex stochastic integrals and providing new distributional bounds.

Contribution

It introduces the first known upper bounds for the distribution of estimators involving triple Wiener-Itô integrals in Vasicek models driven by Gaussian processes.

Findings

Derived Berry-Esséen bounds for moment and least squares estimators.

Extended ratio process analysis to include triple Wiener-Itô integrals.

Established new bounds between estimators' distributions and the Normal distribution.

Abstract

The Berry-Ess\'{e}en upper bounds of moment estimators and least squares estimators of the mean and drift coefficients in Vasicek models driven by general Gaussian processes are studied. When studying the parameter estimation problem of Ornstein-Uhlenbeck (OU) process driven by fractional Brownian motion, the commonly used methods are mainly given by Kim and Park, they show the upper bound of Kolmogorov distance between the distribution of the ratio of two double Wiener-It\^{o} stochastic integrals and the Normal distribution. The main innovation in this paper is extending the above ratio process, that is to say, the numerator and denominator respectively contain triple Wiener-It\^{o} stochastic integrals at most. As far as we know, the upper bounds between the distribution of above estimators and the Normal distribution are novel.