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7 papers · 1 filter
Level numbers preserving transformations on excursionsdefined by random walks with state dependent jump laws
Thierry Huillet, Servet Martinez
We study the number of individuals per level defined by excursions of random walks with state dependent jump law. These level numbersdetermine the probability of the excursion, and…
Sterile versus prolific individuals pertaining to linear-fractional Bienaym{é}-Galton-Watson trees
Thierry Huillet, Servet Martinez
In a Bienaymé-Galton-Watson process for which there is a positiveprobability for individuals of having no offspring, there is a subtlebalance and dependence between the sterile nod…
Taylor's Law for some infinitely divisible probabbility distributions from population models
Joel E. Cohen, Thierry E Huillet
In a family of random variables, Taylor's law or Taylor's power law offluctuation scaling is a variance function that gives the variance of a random variable (rv) wit…
Scaling features of two special Markov chains involving total disasters
Branda Goncalves, Thierry Huillet
Catastrophe Markov chain population models have received a lot of attention in the recent past. We herewith consider two special cases of such models involving total disasters, bot…
Truncation in Duality and Intertwining Kernels
Thierry Huillet, Servet Martinez
We study properties of truncations in the dual and intertwining process in the monotone case. The main properties are stated for the time-reversed process and the time of absorptio…
On the genealogy and coalescence times of Bienaymé-Galton-Watson branching processes
Nicolas Grosjean, Thierry Huillet
Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus o…