Theory of Probability and Mathematical Statistics
Gaussian Volterra processes: Asymptotic growth and statistical estimation
Yuliya Mishura, Kostiantyn Ralchenko and 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.
Keywords: Gaussian Volterra process, asymptotic growth, long- and short-range dependence, parameter estimation, Ornstein–Uhlenbeck process
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