Smaller population size at the MRCA time for stationary branching processes

We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population..

If we loose track of the genealogy, the new population of type 1 can be seen as an immigra- tion process with rate proportional to the size of the Eve-population, the population of

For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove that, up to a deterministic time- change, it

In the second case, no finite population size is assumed, but the gain from future patients is geometrically discounted, so that the gain from patient j if they receive treatment i is

Section 3 is devoted to the description via a Poisson point measure of the ancestral process of the extant population at time 0 and Section 4 gives the different simulations of

Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

In order to follow the coalescences in the ancestral lineages and to describe the backward genealogy of the population, we dene non- exchangeable Markovian coalescent processes

We then introduce some estimates for the asymptotic behaviour of random walks conditioned to stay below a line, and prove their extension to a generalized random walk where the law