Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 422
Kolmogorov bounds in the CLT of the LSE for Gaussian Ornstein Uhlenbeck processes
Rachid Belfadli, Maoudo Faramba Baldé, Khalifa Es-Sebaiy
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 31, 2022
March 03, 2355
April 15, 2355

Abstract: In the present paper we consider the Ornstein-Uhlenbeck (OU) process defined as solution to the equation $dX_{t} = -\theta X_{t}dt+dG_t, \ X_{0}=0$, where $\{G_t,t\geq0\}$ is a Gaussian process with stationary increments, whereas $\theta>0$ is unknown parameter to be estimated. We provide an upper bound in Kolmogorov distance for normal approximation of the least squares estimator of the drift parameter $\theta$ on the basis of the continuous observation $\{X_t,t\in[0,T]\}$, as $T\rightarrow\infty$. Our method is based on a combination of Malliavin calculus and Stein's ...