New explicit examples of fixed points of Poisson shot noise transforms

Details New explicit examples of fixed points of Poisson shot noise transforms New explicit examples of fixed points of Poisson shot noise transforms

2002-02-05

arxiv.org/abs/math/0202035v2

Mathematics

Probability

12 pages

Scientific paper

We show that gamma distributions, generalized positive Linnik distributions, S2 distributions are fixed points of Poisson shot noise transforms. The corresponding response functions are identified via their inverse functions except for some special cases when those can be obtained explicitly. As a by-product, it is proven that log-convexity of the response function is not necessary for selfdecomposability of non-negative Poisson shot noise distribution. Some attention is given to perpetuities of a rather special type which are closely related to our model. In particular, we study the problem of their existence and uniqueness.

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