On maximum likelihood estimation of the drift matrix of a degenerated O–U process

Abstract

In this work, we consider a 2n-dimension Ornstein–Uhlenbeck (O–U) process with a singular diffusion matrix. This process represents a currently used model for mechanical systems subject to random vibrations. We study the problem of estimating the drift parameters of the stochastic differential equation that governs the O–U process. The maximum likelihood estimator proposed and explored in Koncz (J Anal Math 13(1):75–91, 1987) is revisited and applied to our model. We prove the local asymptotic normality property and the convergence of moments of the estimator. Simulation studies based on representative examples taken from the literature illustrate the obtained theoretical results.