Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
Gloter, Arnaud; Gloter Arnaud; 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: gloter@math.univ-mlv.fr
Журнал:
ESAIM: Probability and Statistics
Дата:
2000
Аннотация:
Let (X<sub>t</sub> ) be a diffusion on the interval (l,r) and Δ<sub>n</sub> a sequence of positive numbers tending to zero. We define J <sub> i </sub> as the integral between iΔ<sub>n</sub> and (i + 1)Δ<sub>n</sub> of X <sub> s </sub>. We give an approximation of the law of (J<sub>0</sub>,...,J<sub>n-1</sub>) by means of a Euler scheme expansion for the process (J<sub>i</sub> ). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When Δ<sub>n</sub> = n<sup>-1</sup> we deduce from this expansion estimators of the diffusion coefficient of X based on (J<sub>i</sub> ). These estimators are shown to be asymptotically mixed normal as n tends to infinity.
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