Statistical inference for Vasicek-type model driven by self-similar Gaussian processes

摘要

In this paper, we consider the drift parameters estimation problem for the Vasicek-type model defined asdX(t) = a(b - X-t)d(t) + dG(t), X-0 = 0, t = 0,where a0 and b is an element of R are considered as unknown drift parameters and G(t) is a self-similar Gaussian process with index L is an element of (1/2, 1). We provide sufficient conditions, based on the properties of G, ensuring the strong consistency and the asymptotic distributions of our estimators of (a)over cap and of b based on the observation as {X-t}t is an element of[0,T] as T - infinity. Our approach extend the result of Xiao and Yu (2017) for the case when G is a fractional Brownian motion with Hurst parameter H is an element of (1/2, 1) . We also discuss the cases of sub-fractional Browian motion and bi-fractional Brownian motion. The conclusion can also be extended to more general self-similarity processes, such as Hermite processes.