On some functional of the hybrid process in random scenery

Sergio Alvarez-Andrade

doi:10.1016/j.crma.2009.12.001

Probability Theory

On some functional of the hybrid process in random scenery
[Sur une fonctionnelle du processus hybride en environnement aléatoire]

Présenté par : Paul Malliavin

Sergio Alvarez-Andrade ¹

¹ Laboratoire de mathématiques appliquées, université de technologie de Compiègne, B.P. 529, 60205 Compiègne cedex, France

Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 181-184.

Résumé
Abstract

Dans ce travail nous établissons une borne supérieure dans l'approximation forte d'une fonctionnelle basée sur la marche aléatoire de Kesten–Sptizer en environnement aléatoire, lorsque la marche aléatoire symétrique est remplacée par un processus hybride empirique et des sommes partielles.

In this work we wish to investigate an example based on the so-called Kesten–Spitzer random walk in random scenery. Namely, replacing the one-dimensional random walk in a general i.i.d. scenery by the hybrids of empirical and partial sums process (see, for instance, [L. Horváth, Approximations for hybrids of empirical and partial sums process, J. Statist. Plann. Inference 88 (2000) 1–18]), we establish an upper bound in the strong approximation for the corresponding functional.

Reçu le : 2009-11-19
Accepté le : 2009-11-21
Publié le : 2009-12-29

DOI : 10.1016/j.crma.2009.12.001

Affiliations des auteurs :

Sergio Alvarez-Andrade ¹

¹ Laboratoire de mathématiques appliquées, université de technologie de Compiègne, B.P. 529, 60205 Compiègne cedex, France

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     title = {On some functional of the hybrid process in random scenery},
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Sergio Alvarez-Andrade. On some functional of the hybrid process in random scenery. Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 181-184. doi : 10.1016/j.crma.2009.12.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.12.001/

Bibliographie
Cité par

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[3] X. Chen, D. Khoshnevisan, From charged polymers to random walk in random scenery, http://www.math.utah.edu/~davar/PPT/, preprint, 2008

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