Some Applications of the Mellin Transform to Branching Processes
نویسنده
چکیده
We introduce a Mellin transform of functions which live on all of R 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. AMS (2000) subject classification. 44A05, 60J80.
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