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June 2003 Regular variation in the mean and stable limits for Poisson shot noise
Claudia Klüppelberg, Thomas Mikosch, Anette Schärf
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Bernoulli 9(3): 467-496 (June 2003). DOI: 10.3150/bj/1065444814


Poisson shot noise is a natural generalization of a compound Poisson process when the summands are stochastic processes starting at the points of the underlying Poisson process. We study the limiting behaviour of Poisson shot noise when the limits are infinite-variance stable processes. In this context a sufficient condition for this convergence turns up which is closely related to multivariate regular variation -- we call it regular variation in the mean. We also show that the latter condition is necessary and sufficient for the weak convergence of the point processes constructed from the normalized noise sequence and also for the weak convergence of its extremes.


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Claudia Klüppelberg. Thomas Mikosch. Anette Schärf. "Regular variation in the mean and stable limits for Poisson shot noise." Bernoulli 9 (3) 467 - 496, June 2003.


Published: June 2003
First available in Project Euclid: 6 October 2003

zbMATH: 1044.60013
MathSciNet: MR1997493
Digital Object Identifier: 10.3150/bj/1065444814

Keywords: Extremes , infinitely divisible \rm dst , Poisson random measure , self-similar process , Stable process , weak convergence

Rights: Copyright © 2003 Bernoulli Society for Mathematical Statistics and Probability


Vol.9 • No. 3 • June 2003
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