Gaussian Volterra processes: asymptotic growth and statistical estimation
Statistics Theory
2023-02-08 v1 Probability
Statistics Theory
Abstract
The paper is devoted to three-parametric self-similar Gaussian Volterra processes that generalize fractional Brownian motion. We study the asymptotic growth of such processes and the properties of long- and short-range dependence. Then we consider the problem of the drift parameter estimation for Ornstein-Uhlenbeck process driven by Gaussian Volterra process under consideration. We construct a strongly consistent estimator and investigate its asymptotic properties. Namely, we prove that it has the Cauchy asymptotic distribution.
Cite
@article{arxiv.2302.03363,
title = {Gaussian Volterra processes: asymptotic growth and statistical estimation},
author = {Yuliya Mishura and Kostiantyn Ralchenko and Sergiy Shklyar},
journal= {arXiv preprint arXiv:2302.03363},
year = {2023}
}
Comments
19 pages