On fixed points of Poisson shot noise transforms

2002/09/30 by Aleksander M. Iksanov, Zbigniew J. Jurek
Mathematics · #math.PR #msc:60E07 #msc:60K05

paper · pdf

published as Advances in Applied Probability, 34, no.4, pp.798-825, 2002

arxiv created 2003/02/16 · arxiv updated 2009/11/30

Abstract

Distributional fixed points of a Poisson shot noise transform (for nonnegative, nonincreasing response functions bounded by 1) are characterized. The tail behavior of fixed points is described. Typically they have either exponential moments or their tails are proportional to a power function, with exponent greater than -1. The uniqueness of fixed points is also discussed. Finally, it is proved that in most cases fixed points are absolutely continuous, apart from the possible atom at zero.

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