[Test dʼajustement dʼun processus de diffusion à changement de régime]
Nous considérons un test dʼajustement de Cramér–von Mises dʼun processus de diffusion dont la dérive est de type signe. Il est montré que la distribution limite du test statistique proposé est définie par une fonctionnelle de type intégrale dʼun processus gaussien continu. Nous obtenons la décomposition de Karhunen–Loève du processus limite correspondant et nous montrons que les fonctions propres de cette décompositon ont des expressions en termes de fonctions de Bessel. La représentation de la statistique limite nous permet de trouver le seuil.
We study the asymptotic behavior of the Cramér–von Mises type statistic in the goodness-of-fit hypotheses testing problem for ergodic diffusion processes. The basic (simple) hypothesis is defined by the stochastic differential equation with sign-type trend coefficient and known diffusion coefficient. It is shown that the limit distribution of the proposed test statistic (under hypothesis) is defined by the integral type functional of continuous Gaussian process. We provide the Karhunen–Loève expansion of the corresponding limiting process and show that the eigenfunctions in this expansion are expressed in terms of Bessel functions. This representation for the limit statistic allows us to approximate the threshold.
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@article{CRMATH_2011__349_15-16_897_0,
author = {Gassem, Anis},
title = {On the goodness-of-fit testing for a switching diffusion process},
journal = {Comptes Rendus. Math\'ematique},
pages = {897--900},
publisher = {Elsevier},
volume = {349},
number = {15-16},
year = {2011},
doi = {10.1016/j.crma.2011.06.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.06.010/}
}
TY - JOUR AU - Gassem, Anis TI - On the goodness-of-fit testing for a switching diffusion process JO - Comptes Rendus. Mathématique PY - 2011 SP - 897 EP - 900 VL - 349 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.06.010/ DO - 10.1016/j.crma.2011.06.010 LA - en ID - CRMATH_2011__349_15-16_897_0 ER -
%0 Journal Article %A Gassem, Anis %T On the goodness-of-fit testing for a switching diffusion process %J Comptes Rendus. Mathématique %D 2011 %P 897-900 %V 349 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.06.010/ %R 10.1016/j.crma.2011.06.010 %G en %F CRMATH_2011__349_15-16_897_0
Gassem, Anis. On the goodness-of-fit testing for a switching diffusion process. Comptes Rendus. Mathématique, Tome 349 (2011) no. 15-16, pp. 897-900. doi : 10.1016/j.crma.2011.06.010. http://www.numdam.org/articles/10.1016/j.crma.2011.06.010/
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