https://doi.org/10.1140/epjp/s13360-021-01738-9
Regular Article
Optimal rates for the parameter prediction of a Gaussian Vasicek process
1
School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074, Wuhan, Hubei, People’s Republic of China
2
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, Pakistan
3
Department of Mathematics, Faculty of Science and Health, Koya University, KOY45, Kurdistan Region - F. R., Koya, Iraq
4
Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria
5
Faculty of Exact Sciences and Informatics, Mathematic Department, Hassiba Benbouali University, Chlef, Algeria
d s.djilali@univ-chlef.dz, djilali.salih@yahoo.fr
Received:
25
May
2021
Accepted:
7
July
2021
Published online:
6
August
2021
In this article, we deal with statistical estimation problems of drift parameters of a Vasicek-type model that is perturbed by Gaussian noise that is defined via 
with unknown parameters 
and 
, where G is a Gaussian process with index 
. Based on discrete observations and using tools from Malliavin calculus together with Nordin–Peccati analysis, we provide estimators 
of 
and 
of 
. Moreover, the strong consistency and asymptotic normality of our estimators have been established using the properties of G. The rates of convergence in total variation for a sequence of random variables living in a fixed Wiener chaos are computed. Finally, we discuss the case when the process G is replaced by a fractional Brownian motion.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
