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Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient

Published online by Cambridge University Press:  15 August 2002

Arnaud Gloter
Arnaud Gloter*
Affiliation:
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 protected]
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Abstract

Let (Xt ) be a diffusion on the interval (l,r) and Δn a sequence of positive numbers tending to zero. We define J i as the integral between iΔn and (i + 1)Δn of X s .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 anexplicit Gaussian ARMA(1,1) process is obtained.When Δn = n-1 we deduce from this expansion estimatorsof the diffusion coefficient of X based on (Ji ). These estimatorsare shown to be asymptotically mixed normal as n tends to infinity.

Keywords

Diffusion processesdiscrete time observationhidden markov model.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 4 , 2000 , pp. 205 - 227
Copyright
© EDP Sciences, SMAI, 2000

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