Gaussian Volterra processes: Asymptotic growth and statistical estimation

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.

Asymptotic Growth of Sample Paths of Tempered Fractional Brownian Motions, with Statistical Applications to Vasicek-Type Models

“…Remark 13. The estimation of b for known a = 0 was investigated in [26], Section 4. Note that, in this case, the additional condition (56) is not required, cf.…”

Combinatorial approach to the calculation of projection coefficients for the simplest Gaussian-Volterra process

“…First, such kernels are very particular, therefore, it is natural to consider their generalizations and investigate the properties of such generalized GVp's. This was, in particular, done in the papers [16,12,10,15]. Second, the kernels (1), ( 2) are comparatively complicated.…”