Comptes Rendus
no. 7
Probability Theory
Convergence in law for certain additive functionals of symmetric stable processes under strong topology
[Convergence en loi pour certaines fonctionnelles additives d'un processus stable symétrique sous une topologie forte]

Présenté par : Marc Yor

Mohamed Ait Ouahra1
1 Departement of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, B.P. 2390, Marrakech 40.001, Morocco
Comptes Rendus. Mathématique, Volume 340 (2005) no. 7, pp. 519-524.

Nous donnons certains théorèmes limites pour certaines fonctionnelles additives d'un processus stable symétrique d'indice 1<α⩽2 dans une classe d'espace de Besov anisotropique. Ces résultats généralisent ceux obtenus par Eisenbaum (1997) et par Csaki et al. (2002).

We give some limit theorems of certain additive functionals for symmetric stable process of index 1<α⩽2 in anisotropic Besov space. These results generalize those obtained by Eisenbaum (1997) and by Csaki et al. (2002).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.02.013

Mohamed Ait Ouahra 1

1 Departement of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, B.P. 2390, Marrakech 40.001, Morocco 
@article{CRMATH_2005__340_7_519_0,
     author = {Mohamed Ait Ouahra},
     title = {Convergence in law for certain additive functionals of symmetric stable processes under strong topology},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {519--524},
     publisher = {Elsevier},
     volume = {340},
     number = {7},
     year = {2005},
     doi = {10.1016/j.crma.2005.02.013},
     language = {en},
}
TY  - JOUR
AU  - Mohamed Ait Ouahra
TI  - Convergence in law for certain additive functionals of symmetric stable processes under strong topology
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 519
EP  - 524
VL  - 340
IS  - 7
PB  - Elsevier
DO  - 10.1016/j.crma.2005.02.013
LA  - en
ID  - CRMATH_2005__340_7_519_0
ER  - 
%0 Journal Article
%A Mohamed Ait Ouahra
%T Convergence in law for certain additive functionals of symmetric stable processes under strong topology
%J Comptes Rendus. Mathématique
%D 2005
%P 519-524
%V 340
%N 7
%I Elsevier
%R 10.1016/j.crma.2005.02.013
%G en
%F CRMATH_2005__340_7_519_0
Mohamed Ait Ouahra. Convergence in law for certain additive functionals of symmetric stable processes under strong topology. Comptes Rendus. Mathématique, Volume 340 (2005) no. 7, pp. 519-524. doi : 10.1016/j.crma.2005.02.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.02.013/

[1] M. Ait Ouahra, Weak convergence to fractional Brownian motion in some anisotropic Besov space, Ann. Blaise Pascal (2003), in press

[2] M. Ait Ouahra; M. Eddahbi Théorèmes limites pour certaines fonctionnelles associées aux processus stables sur l'espace de Hölder, Publ. Math., Volume 45 (2001), pp. 371-386

[3] B. Boufoussi; E.H. Lakhel Un résultat d'approximation d'une EDPS hyperbolique en norme de Besov anisotropic, C. R. Acad. Sci. Paris, Ser. I, Volume 330 (2000), pp. 883-888

[4] E.S. Boylan Local times for a class of Markov Processes, Illinois J. Math., Volume 8 (1964), pp. 19-39

[5] P. Billingsley Convergence of Probability Measures, Wiley, New York, 1968

[6] E. Csaki; Z. Shi; M. Yor Fractional Brownian motion as “higher-order” fractional derivatives of Brownian local times, Limit Theorems in Probability and Statistics, vol. I (Balatonlelle, 1999), Jânos Bolyai Math. Soc., Budapest, 2002, pp. 365-387

[7] N. Eisenbaum Théorèmes limites pour les temps locaux d'un processus stable symetrique, Séminaire de Probab., XXXI, Lecture Notes in Math., vol. 1655, 1997, pp. 216-224

[8] A. Kamont Isomorphism of some anisotropic Besov and sequence spaces, Studia Math., Volume 110 (1994) no. 2, pp. 169-189

[9] A. Kamont On the fractional anisotropic Wiener field, Probab. Math. Statist., Volume 16 (1996) no. 1, pp. 85-98

[10] J. Lamperti On convergence of stochastic processes, Trans. Amer. Math. Soc., Volume 104 (1962), pp. 430-435

[11] M.B. Marcus; J. Rosen p-variation of the local times of symmetric stable processes and of Gaussian processes with stationary increments, Ann. Probab., Volume 20 (1992) no. 4, pp. 1685-1713

[12] S.G. Samko; A.A. Kilbas; O.I. Marichev Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science, 1993

[13] M. Yor Le drap Brownien comme limite en loi de temps locaux linéaires (J. Azéma; P.A. Meyer; M. Yor, eds.), Séminaire Probab. XVII, Lect. Notes in Math., vol. 986, Springer, Berlin, 1983, pp. 89-105

Cité par Sources :

Commentaires - Politique