We consider a weighted random ball model generated by a Poisson measure. The macroscopic behaviour of the weight amassed on this model by a configuration has recently received attention. In this paper, we complement the previous finite dimensional distribution fluctuation results and propose functional convergences of such functionals on the set of configurations.
DOI : 10.1051/ps/2015016
Mots clés : Self-similarity, generalized random fields, functional convergence, tightness, Poisson point process
@article{PS_2015__19__782_0,
author = {Breton, Jean-Christophe and Gobard, Renan},
title = {Infinite dimensional functional convergences in random balls model},
journal = {ESAIM: Probability and Statistics},
pages = {782--793},
publisher = {EDP-Sciences},
volume = {19},
year = {2015},
doi = {10.1051/ps/2015016},
zbl = {1333.60061},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2015016/}
}
TY - JOUR AU - Breton, Jean-Christophe AU - Gobard, Renan TI - Infinite dimensional functional convergences in random balls model JO - ESAIM: Probability and Statistics PY - 2015 SP - 782 EP - 793 VL - 19 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2015016/ DO - 10.1051/ps/2015016 LA - en ID - PS_2015__19__782_0 ER -
%0 Journal Article %A Breton, Jean-Christophe %A Gobard, Renan %T Infinite dimensional functional convergences in random balls model %J ESAIM: Probability and Statistics %D 2015 %P 782-793 %V 19 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2015016/ %R 10.1051/ps/2015016 %G en %F PS_2015__19__782_0
Breton, Jean-Christophe; Gobard, Renan. Infinite dimensional functional convergences in random balls model. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 782-793. doi : 10.1051/ps/2015016. http://archive.numdam.org/articles/10.1051/ps/2015016/
, and , Self-similar random fields and rescaled random balls models. J. Theoret. Probab. 23 (2010) 1110–1141. | Zbl
and , Rescaled weighted random balls models and stable self-similar random fields. Stochastic Process. Appl. 119 (2009) 3633–3652. | Zbl
and , Functional macroscopic behavior of weighted random ball model. Alea, Lat. Am. J. Probab. Math. Stat. 8 (2011) 177–196. | Zbl
H. Brézis, Analyse fonctionnelle. Masson (1983). | Zbl
W. Feller, An Introduction to Probability Theory and its Applications. Wiley (1966), Vol. 2. | Zbl
I. Kaj, Aspects of wireless network modeling based on Poisson point processes Fields. Institute Workshop on Applied Probability, Carleton University. Available at: http://www.math.uu.se/ĩkaj/preprints/wirelessnotes2.pdf (2006).
, , and , Scaling limits for random fields with long-range dependence. Ann. Probab. 35 (2007) 528–550. | Zbl
O. Kallenberg, Foundations of Modern Probability, 2nd edition. Springer, New-York (2002). | Zbl
, , and , Is network traffic approximated by stable Lévy motion of fractional Brownian motion. Ann. Appl. Probab. 12 (2002) 23–68. | Zbl
G. Samorodnitsky and M.S. Taqqu, Stable non-Gaussian random processes. Stochastic Modeling, Chapman & Hall (1994). | Zbl
M. Shaked and G. Shanthikumar, Stochastic orders and their applications. Probability and Mathematical Statistics. Academic Press (1994). | Zbl
and , Inequalities for the th absolute moment of a sum of random variables, . Ann. Math. Statist. 36 (1965) 299–303. | Zbl
and , Co-Channel interference modeling in a Poisson field of interferers in wireless communications. IEEE Trans. Signal Process. 51 (2003) 64–76. | Zbl
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