Mathematics – Probability
Scientific paper
2002-09-02
Advances in Applied Probability, 34, no.4, pp.798-825, 2002
Mathematics
Probability
Scientific paper
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.
Iksanov Aleksander M.
Jurek Zbigniew J.
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