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

In this paper, we consider the drift parameters estimation problem for the Vasicek-type model defined as d X t = a (b − X t) d t + d G t , X 0 = 0 , t ≥ 0 where a < 0 and b ∈ R are considered as unknown drift parameters and G_t is a self-similar Gaussian process with index L ∈ (1 / 2 , 1) . We provide sufficient conditions, based on the properties of G, ensuring the strong consistency and the asymptotic distributions of our estimators a ̂ of a and b ̂ of b based on the observation { X t } t ∈ [ 0 , T ] as T → ∞ . Our approach extend the result of Xiao and Yu (2017) for the case when G is a fractional Brownian motion with Hurst parameter H ∈ (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. [ABSTRACT FROM AUTHOR]