Comptes Rendus
no. 3-4
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-Andrade1
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.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.12.001
Sergio Alvarez-Andrade 1

1 Laboratoire de mathématiques appliquées, université de technologie de Compiègne, B.P. 529, 60205 Compiègne cedex, France 
@article{CRMATH_2010__348_3-4_181_0,
     author = {Sergio Alvarez-Andrade},
     title = {On some functional of the hybrid process in random scenery},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {181--184},
     publisher = {Elsevier},
     volume = {348},
     number = {3-4},
     year = {2010},
     doi = {10.1016/j.crma.2009.12.001},
     language = {en},
}
TY  - JOUR
AU  - Sergio Alvarez-Andrade
TI  - On some functional of the hybrid process in random scenery
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 181
EP  - 184
VL  - 348
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crma.2009.12.001
LA  - en
ID  - CRMATH_2010__348_3-4_181_0
ER  - 
%0 Journal Article
%A Sergio Alvarez-Andrade
%T On some functional of the hybrid process in random scenery
%J Comptes Rendus. Mathématique
%D 2010
%P 181-184
%V 348
%N 3-4
%I Elsevier
%R 10.1016/j.crma.2009.12.001
%G en
%F CRMATH_2010__348_3-4_181_0
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/

[1] S. Alvarez-Andrade Some asymptotic properties of the hybrids of empirical and partial-sum processes, Rev. Mat. Iberoamericana, Volume 24 (2008), pp. 31-41

[2] R. Bass; D. Khoshnevisan Laws of the iterated logarithm for local times of the empirical process, Ann. Probab., Volume 23 (1995), pp. 388-399

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

[4] E. Csáki; M. Csörgő; A. Földes; P. Révész The local time of iterated Brownian motion, J. Theoret. Probab., Volume 9 (1996), pp. 717-743

[5] E. Csáki; W. König; Z. Shi An embedding for the Kesten–Spitzer random walk in random scenery, Stochastic Process. Appl., Volume 82 (1999), pp. 283-292

[6] M. Csörgő; Z. Shi; M. Yor Some asymptotics properties of the local time of the uniform empirical processes, Bernoulli, Volume 5 (1999), pp. 1035-1058

[7] J. Diebolt A non-parametric test for the regression function: Asymptotic theory, J. Statist. Plann. Inference, Volume 44 (1995), pp. 1-17

[8] L. Horváth Approximations for hybrids of empirical and partial sums process, J. Statist. Plann. Inference, Volume 88 (2000), pp. 1-18

[9] H. Kesten An iterated logarithm law for local time, Duke Math. J., Volume 32 (1965), pp. 447-456

[10] D. Khoshnevisan Level crossings for the empirical process, Stochastic Process. Appl., Volume 43 (1992), pp. 331-343

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

On the quantile process under progressive censoring

Sergio Alvarez-Andrade

C. R. Math (2009)