26 citations · 59 across the 24 of their papers we have counts for
29 papers
Threatening excursions in large population quasi-stationary birth and death systems. On a question of Antonio Galves
Pierre Collet, Servet Martínez, Sylvie Méléard
We consider time continuous multispecies birth and death processes in a regime of large populations. The jump rates depend on a large scaling parameter K modeling the charge capaci…
A simple finite delayed multi-type branching process for infectious disease modeling
Andrew Hart, Servet Martínez
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represe…
Inverse M-matrix, a new characterization
Claude Dellacherie, Servet Martinez, Jaime San Martin
In this article we present a new characterization of inverse M-matrices, inverse row diagonally dominant M-matrices and inverse row and column diagonally dominant M-matrices, based…
Revisiting John Lamperti's maximal branching process
Thierry Huillet, Servet Martinez
Lamperti's maximal branching process is revisited, with emphasis on the description of the shape of the invariant measures in both the recurrent and transient regimes. A truncated…
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…
Quasi-Stationary Distributions and Resilience: What to get from a sample?
J. -R. Chazottes, P. Collet, S. Martínez +1
We study a class of multi-species birth-and-death processes going almost surely to extinction and admitting a unique quasi-stationary distribution (qsd for short). When rescaled by…