| Автор | Gloter, Arnaud |
| Дата выпуска | 2000 |
| dc.description | 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. |
| Формат | application.pdf |
| Издатель | EDP Sciences |
| Копирайт | © EDP Sciences, SMAI, 2000 |
| Тема | Diffusion processes |
| Тема | discrete time observation |
| Тема | hidden markov model. |
| Название | Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient |
| Тип | research-article |
| DOI | 10.1051/ps:2000105 |
| Electronic ISSN | 1262-3318 |
| Print ISSN | 1292-8100 |
| Журнал | ESAIM: Probability and Statistics |
| Том | 4 |
| Первая страница | 205 |
| Последняя страница | 227 |
| Аффилиация | 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 |
