On the spread of a branching Brownian motion whose offspring number has infinite variance
Abstract
We study the impact on shape parameters of an underlying Bienaym\'e-Galton-Watson branching process (height, width and first hitting time), of having a non-spatial branching mechanism with infinite variance. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM) we then consider spatial branching processes in dimension d, not necessarily integer. The underlying branching mechanism is then either a binary branching model or one presenting infinite variance. In particular we evaluate the chance p(x) of being hit if the epidemics started away at distance x. We compute the large x tail probabilities of this event, both when the branching mechanism is regular and when it exhibits very large fluctuations.
Keywords
Cite
@article{arxiv.1402.5389,
title = {On the spread of a branching Brownian motion whose offspring number has infinite variance},
author = {Jean Avan and Nicolas Grosjean and Thierry Huillet},
journal= {arXiv preprint arXiv:1402.5389},
year = {2014}
}