Rescaled weighted random ball models and stable self-similar random fields

DOI10.1016/j.spa.2009.06.010zbMath1175.60049arXiv0807.4700OpenAlexW1978700040MaRDI QIDQ734656

Jean-Christophe Breton, Clément Dombry

Publication date: 13 October 2009

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.4700

zbMATH Keywords

self-similarityPoisson point processgeneralized random fieldsstable field

Mathematics Subject Classification ID

Random fields (60G60) Central limit and other weak theorems (60F05) Stable stochastic processes (60G52)

Related Items (13)

Poisson sphere counting processes with random radii ⋮ Rescaled weighted determinantal random balls ⋮ On the convergence of a multidimensional workload in a service system to a stable process ⋮ Random balls model with dependence ⋮ Macroscopic analysis of determinantal random balls ⋮ Generalized operator-scaling random ball model ⋮ On stochastic models of teletraffic with heavy-tailed distributions ⋮ Infinite dimensional functional convergences in random balls model ⋮ Scaling limits for a random boxes model ⋮ Micropulses and Different Types of Brownian Motion ⋮ Scaling limits of solutions of linear stochastic differential equations driven by Lévy white noises ⋮ Macroscopic analysis of shot-noise Cox random balls ⋮ A generalisation of the fractional Brownian field based on non-Euclidean norms

Cites Work

• Is network traffic approximated by stable Lévy motion or fractional Brownian motion?
• Scaling limits for random fields with long-range dependence
• Poisson random balls: self-similarity and X-ray images
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