Convergence in variation of the laws of multiple stable integrals

Jean-Christophe Breton

doi:10.1016/j.crma.2003.11.020

Probability Theory

Convergence in variation of the laws of multiple stable integrals

Presented by: Marc Yor

Jean-Christophe Breton ¹

¹ Laboratoire de mathématiques et applications, Université de La Rochelle, avenue Michel Crépeau, 17042 La Rochelle cedex, France

Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 239-244.

Abstract
Résumé

Multiple stable integrals generalize Wiener–Itô integrals, their construction being based upon a generalized LePage representation. This approach allows one to study their behaviour. We are interested in this Note in the continuity for total variation norm of the laws of these integrals I_d(f) with respect to f.

Les intégrales stables multiples généralisent celles de Wiener–Itô, leur construction est fondée sur une représentation de LePage généralisée. Cette approche permet d'étudier leur loi. Nous nous intéressons dans cette Note à la continuité pour la variation totale des lois de ces intégrales I_d(f) par rapport à f.

Received: 2002-12-01
Accepted: 2003-11-17
Published online: 2003-12-24

DOI: 10.1016/j.crma.2003.11.020

Author's affiliations:

Jean-Christophe Breton ¹

¹ Laboratoire de mathématiques et applications, Université de La Rochelle, avenue Michel Crépeau, 17042 La Rochelle cedex, France

@article{CRMATH_2004__338_3_239_0,
     author = {Jean-Christophe Breton},
     title = {Convergence in variation of the laws of multiple stable integrals},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {239--244},
     publisher = {Elsevier},
     volume = {338},
     number = {3},
     year = {2004},
     doi = {10.1016/j.crma.2003.11.020},
     language = {en},
}

TY  - JOUR
AU  - Jean-Christophe Breton
TI  - Convergence in variation of the laws of multiple stable integrals
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 239
EP  - 244
VL  - 338
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crma.2003.11.020
LA  - en
ID  - CRMATH_2004__338_3_239_0
ER  -

%0 Journal Article
%A Jean-Christophe Breton
%T Convergence in variation of the laws of multiple stable integrals
%J Comptes Rendus. Mathématique
%D 2004
%P 239-244
%V 338
%N 3
%I Elsevier
%R 10.1016/j.crma.2003.11.020
%G en
%F CRMATH_2004__338_3_239_0

Jean-Christophe Breton. Convergence in variation of the laws of multiple stable integrals. Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 239-244. doi : 10.1016/j.crma.2003.11.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.020/

References
Cited by

[1] J.-C. Breton Multiple stable stochastic integrals: series representation and absolute continuity of their law, J. Theoret. Probab., Volume 15 (2002) no. 4, pp. 877-901

[2] Y.A. Davydov; M.A. Lifshits; N.V. Smorodina Local Properties of Distributions of Stochastic Functionals, American Mathematical Society, 1998

[3] Y.A. Davydov; G.V. Martynova Limit Behavior of Multiple Stochastic Integral, Nauka, Moscow, 1989 pp. 55–57 (en Russe)

[4] S. Kwapien; W. Woyczynski Random Series and Stochastic Integrals. Single and Multiple Martingale Methods, Birkhäuser, 2001

[5] G. Samorodnitsky; J. Szulga An asymptotic evaluation of the tail of a multiple symmetric α-stable integral, Ann. Probab., Volume 17 (1989), pp. 1503-1520

[6] G. Samorodnitsky; M.S. Taqqu Stable Non-Gaussian Random Processes, Chapman and Hall, 1994

Cited by Sources:

Comments - Policy