[Sur une fonctionnelle du processus hybride en environnement aléatoire]
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.
Accepté le :
Publié le :
@article{CRMATH_2010__348_3-4_181_0,
author = {Alvarez-Andrade, Sergio},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.12.001/}
}
TY - JOUR AU - Alvarez-Andrade, Sergio 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2009.12.001/ DO - 10.1016/j.crma.2009.12.001 LA - en ID - CRMATH_2010__348_3-4_181_0 ER -
%0 Journal Article %A Alvarez-Andrade, Sergio %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 %U http://www.numdam.org/articles/10.1016/j.crma.2009.12.001/ %R 10.1016/j.crma.2009.12.001 %G en %F CRMATH_2010__348_3-4_181_0
Alvarez-Andrade, Sergio. On some functional of the hybrid process in random scenery. Comptes Rendus. Mathématique, Tome 348 (2010) no. 3-4, pp. 181-184. doi : 10.1016/j.crma.2009.12.001. http://www.numdam.org/articles/10.1016/j.crma.2009.12.001/
[1] Some asymptotic properties of the hybrids of empirical and partial-sum processes, Rev. Mat. Iberoamericana, Volume 24 (2008), pp. 31-41
[2] 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] The local time of iterated Brownian motion, J. Theoret. Probab., Volume 9 (1996), pp. 717-743
[5] An embedding for the Kesten–Spitzer random walk in random scenery, Stochastic Process. Appl., Volume 82 (1999), pp. 283-292
[6] Some asymptotics properties of the local time of the uniform empirical processes, Bernoulli, Volume 5 (1999), pp. 1035-1058
[7] A non-parametric test for the regression function: Asymptotic theory, J. Statist. Plann. Inference, Volume 44 (1995), pp. 1-17
[8] Approximations for hybrids of empirical and partial sums process, J. Statist. Plann. Inference, Volume 88 (2000), pp. 1-18
[9] An iterated logarithm law for local time, Duke Math. J., Volume 32 (1965), pp. 447-456
[10] Level crossings for the empirical process, Stochastic Process. Appl., Volume 43 (1992), pp. 331-343
Cité par Sources :
