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arXiv · 0706.2638

Some applications of the Mellin transform to branching processes

Wolfgang P. Angerer
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Abstract

We introduce a Mellin transform of functions which live on all of $\bR$ and discuss its applications to the limiting theory of Bellman-Harris processes, and specifically Luria-Delbrück processes. More precisely, we calculate the life-time distribution of particles in a Bellman-Harris process from their first-generation offspring and limiting distributions, and prove a formula for the Laplace transform of the distribution of types in a Luria-Delbrück process in the Mittag-Leffler limit. As a by-product, we show how to easily derive the (classical) Mellin transforms of certain stable probability distributions from their Fourier transform.

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Wolfgang P. Angerer. 2008-04-16. Some applications of the Mellin transform to branching processes. https://arxiv.org/abs/0706.2638

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