Volume 4, 2000
|Page(s)||205 - 227|
|Published online||15 August 2002|
Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
Université de Marne-la-Vallée, Équipe d'Analyse et de
Mathématiques Appliquées, 5 boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2,
France; e-mail: email@example.com
Revised: 5 April 2000
Let (Xt) be a diffusion on the interval (l,r) and Δn a sequence of positive numbers tending to zero. We define Ji as the integral between iΔn and (i + 1)Δn of Xs. We give an approximation of the law of (J0,...,Jn-1) by means of a Euler scheme expansion for the process (Ji). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When Δn = n-1 we deduce from this expansion estimators of the diffusion coefficient of X based on (Ji). These estimators are shown to be asymptotically mixed normal as n tends to infinity.
Mathematics Subject Classification: 62F12 / 62M09
Key words: Diffusion processes / discrete time observation / hidden markov model.
© EDP Sciences, SMAI, 2000
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