Crossings of smooth shot noise processes

DOI10.1214/11-AAP807zbMath1278.60073arXiv1211.5896OpenAlexW3099258093MaRDI QIDQ1931317

Agnès Desolneux, Hermine Biermé

Publication date: 25 January 2013

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.5896

zbMATH Keywords

characteristic functionPoisson processstationary processlevel crossingsshot noiseinfinitely divisible process

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Characteristic functions; other transforms (60E10) Sample path properties (60G17)

Related Items (12)

On the perimeter of excursion sets of shot noise random fields ⋮ Functional limit theorems for a new class of non-stationary shot noise processes ⋮ Poisson sphere counting processes with random radii ⋮ Mean geometry for 2D random fields: level perimeter and level total curvature integrals ⋮ On the finiteness of the moments of the measure of level sets of random fields ⋮ Asymptotics for the critical level and a strong invariance principle for high intensity shot noise fields ⋮ Functional Limit Theorems for Shot Noise Processes with Weakly Dependent Noises ⋮ A Functional Limit Theorem for the Integrals over Level Sets of a Gaussian Random Field ⋮ Normal convergence of nonlocalised geometric functionals and shot-noise excursions ⋮ Quantitative two-scale stabilization on the Poisson space ⋮ Rice formula for processes with jumps and applications ⋮ Shot noise processes with randomly delayed cluster arrivals and dependent noises in the large-intensity regime

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