On fixed points of Poisson shot noise transforms

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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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Probability, Primary 60E07; Secondary 60K05

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http://salesiana.dossiersoluciones.com/handle/123456789/64827

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0209015
 http://arxiv.org/abs/math/0209015
 Advances in Applied Probability, 34, no.4, pp.798-825, 2002

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arXiv