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

• Autor(a) principal: Ana Prior
• Data de Publicação: 2017
• Outros Autores: Marina Kleptsyna, Paula Milheiro de Oliveira
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://hdl.handle.net/10216/116122
• topic: Estatística, Matemática aplicada, Teoria das probabilidades, Matemática; Statistics, Applied mathematics, Probability theory, Mathematics

In this work, we consider a 2n-dimension OrnsteinUhlenbeck (OU) 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 OU process. The maximum likelihood estimator proposed and explored in Koncz (J Anal Math 13(1):7591, 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. (c) 2016, Springer Science+Business Media Dordrecht.