Geodesic
Infinite dimensional functional convergences in random balls model
Breton, Jean-Christophe1  ; Gobard, Renan1 
1 Institut de recherche mathématique de Rennes (IRMAR), UMR 6625, Université de Rennes 1, Campus de Beaulieu, 263 Avenue du Général Leclerc, 35042 Rennes, France
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 782-793.

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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.

Reçu le :
DOI : 10.1051/ps/2015016
Classification : 60F17, 60G60, 60G18, 60H05
Keywords: Self-similarity, generalized random fields, functional convergence, tightness, Poisson point process

Breton, Jean-Christophe 1 ; Gobard, Renan 1

1 Institut de recherche mathématique de Rennes (IRMAR), UMR 6625, Université de Rennes 1, Campus de Beaulieu, 263 Avenue du Général Leclerc, 35042 Rennes, France 
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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://geodesic.mathdoc.fr/articles/10.1051/ps/2015016/

H. Biermé, A. Estrade and I. Kaj, Self-similar random fields and rescaled random balls models. J. Theoret. Probab. 23 (2010) 1110–1141. | Zbl

J.-C. Breton and C. Dombry, Rescaled weighted random balls models and stable self-similar random fields. Stochastic Process. Appl. 119 (2009) 3633–3652. | Zbl

J.-C. Breton and C. Dombry, 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).

I. Kaj, L. Leskelä, I. Norros and V. Schmidt, 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

T. Mikosch, S. Resnick, H. Rootzén and A. Stegeman, 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

B. Von Bahr and C.-G. Esseen, Inequalities for the rth absolute moment of a sum of random variables, 1≤r≤2. Ann. Math. Statist. 36 (1965) 299–303. | Zbl

X. Yang and A.P. Petropulu, 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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