191 citations · 256 across the 29 of their papers we have counts for
6 papers · 1 filter
Quasi-limiting estimates for periodic absorbed Markov chains
Nicolas Champagnat, Denis Villemonais
We consider periodic Markov chains with absorption. Applying to iterates of this periodic Markov chain criteria for the exponential convergence of conditional distributions of aper…
Binary branching processes with Moran type interactions
Alexander M. G. Cox, Emma Horton, Denis Villemonais
The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, re…
The Multi-type Bisexual Galton-Watson Branching Process
Coralie Fritsch, Denis Villemonais, Nicolás Zalduendo
In this work we study the bisexual Galton-Watson process with a finite number of types, where females and males mate according to a ''mating function'' and form couples of differen…
General diffusion processes as the limit of time-space Markov chains
Alexis Anagnostakis, Antoine Lejay, Denis Villemonais
We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes w…
A quasi-stationary approach to the long-term asymptotics of the growth-fragmentation equation
Denis Villemonais, Alexander Watson
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the…
Quasi-stationary distributions in reducible state spaces
Nicolas Champagnat, Denis Villemonais
We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with…