Parameter maximum likelihood estimation problem for time-periodic-drift Langevin type stochastic differential equations

Dominique Dehay (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we investigate the large-sample behavior of the maximum likelihood estimate (MLE) of the parameter for a process which follows a linear stochastic differential equation whose drift coefficient is the product of an unknown parameter, a periodic-in-time function. We establish the consistency of the MLE, and we study its asymptotic minimax effciency.

Mots clés: Time-inhomogeneous diffusion process; periodicity; Ornstein Uhlenbeck process; efficiency; local asymptotic minimax bound; parametric; maximum likelihood

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Dominique Dehay. Parameter maximum likelihood estimation problem for time-periodic-drift Langevin type stochastic differential equations. 2013. ⟨hal-00794615v1⟩