arXiv subjects

Wolfgang P. Angerer

Publications and source records attributed to Wolfgang P. Angerer.

3 recordsLinked to original sources

arXiv2008

Some applications of the Mellin transform to branching processes

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.

math.PR↗

arXiv2006

Proliferation Model Dependence in Fluctuation Analysis: The Neutral Case

We discuss the evaluation of Luria-Delbrueck fluctuation experiments under Bellman-Harris models of cell proliferation. It is shown that under certain very natural assumptions concerning the life-time distributions and the offspring distributions of mutant and non-mutant bacteria, the suitably normed and centered number of mutants contained in a large culture of bacteria converges to a stable random variable with index 1. The result obtains under the assumption that the mutation under consideration is neutral in the sense that on average, mutant cells produce the same number of offspring as non-mutant cells.

math.PR↗

arXiv2006

On Seneta's constants for the supercritical Bellman-Harris process with $E(Z_+ \log Z_+) = \infty$

For a finite mean supercriticial Bellman-Harris process, there exist numbers $χ_t$ (the Seneta constants) such that $χ_t$ times the size of the population at time $t$ converges almost surely to a non-degenerate limit. We obtain a characterisation of the slowly varying part of the Seneta constants under the assumption that the life-time distribution of particles is strongly non-lattice.

math.PR↗