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arXiv · 2302.03363

Gaussian Volterra processes: asymptotic growth and statistical estimation

Yuliya Mishura·Kostiantyn Ralchenko·Sergiy Shklyar
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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.

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Yuliya Mishura, Kostiantyn Ralchenko, Sergiy Shklyar. 2023-02-07. Gaussian Volterra processes: asymptotic growth and statistical estimation. https://arxiv.org/abs/2302.03363

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