Extremes for shot noise processes with heavy tailed amplitudes

DOI10.2307/3215091zbMath0886.60041OpenAlexW2319163845MaRDI QIDQ4364871

William P. McCormick

Publication date: 18 February 1998

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

Full work available at URL: https://doi.org/10.2307/3215091

zbMATH Keywords

weak convergenceextreme valuesrenewal processesshot noise

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Discrete-time Markov processes on general state spaces (60J05) Special processes (60K99) Renewal theory (60K05)

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On convolution equivalence with applications ⋮ Tail behavior of Poisson shot noise processes under heavy-tailed shocks and actuarial applications ⋮ Prediction in a Poisson cluster model with multiple cluster processes ⋮ Functional limit theorems for a new class of non-stationary shot noise processes ⋮ Prediction in a Poisson cluster model ⋮ Limiting properties of Poisson shot noise processes ⋮ Large deviations for multidimensional state-dependent shot-noise processes ⋮ Inference for shot noise ⋮ Extremes of regularly varying Lévy-driven mixed moving average processes ⋮ Power and exponential moments of the number of visits and related quantities for perturbed random walks

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