Statistical Estimations for Non-Ergodic Vasicek Model Driven by Gaussian Processes

Abstract

We study the joint asymptotic distribution of the least squares estimator of the parameter (θ, μ) in non-ergodic Vasicek models driven by seven specific Gaussian processes. To facilitate the proofs, we derive the inner product formulas of the canonical Hilbert spaces associated to the seven specific Gaussian processes. The integration by parts for normalized bounded variation functions is essential to the inner product formulas. We apply the inner product formulas of the seven Gaussian processes to check the set of conditions of Es-Sebaiy, Es.Sebaiy (2021).