Related papers: A modified lookdown construction for the Xi-Flemin…
The Fleming-Viot (FV) process is a measure-valued diffusion that models the evolution of type frequencies in a countable population which evolves under resampling (genetic drift), mutation, and selection. In the classic FV model the fitness…
We introduce an individual-based model for structured populations undergoing demographic bottlenecks, i.e. drastic reductions in population size that last many generations and can have arbitrary shapes. We first show that the…
We introduce a reversible Markovian coagulation-fragmentation process on the set of partitions of $\{1,\ldots,L\}$ into disjoint intervals. Each interval can either split or merge with one of its two neighbors. The invariant measure can be…
We define a Markov process in a forward population model with backward genealogy given by the $\Lambda$-coalescent. This Markov process, called the fixation line, is related to the block counting process through its hitting times. Two…
We give a de Finetti type representation for exchangeable random coalescent trees (formally described as semi-ultrametrics) in terms of sampling iid sequences from marked metric measure spaces. We apply this representation to define…
This paper provides a new construction of \Lambda-coalescents called "measure division construction". This construction is pathwise and consists of dividing the characteristic measure \Lambda into several parts and adding them one by one to…
Motivated by questions of ergodicity for shift invariant Fleming-Viot process, we consider the centered Fleming-Viot process $\left(Z_{t} \right)_{t\geqslant 0}$ defined by $Z_{t} := \tau_{-\left\langle {\rm id}, Y_{t} \right\rangle} \sharp…
A generalized stepping stone model with $\Xi$-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that Kingman's…
We consider a strong Markov process with killing and prove an approximation method for the distribution of the process conditioned not to be killed when it is observed. The method is based on a Fleming-Viot type particle system with…
This paper investigates the long-term behavior of a class of $\Lambda$-Wright--Fisher processes incorporating frequency-dependent selection, coordinated (bidirectional) selection, as well as individual and coordinated mutation. Our primary…
Fleming-Viot type particle systems represent a classical way to approximate the distribution of a Markov process with killing, given that it is still alive at a final deterministic time. In this context, each particle evolves independently…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
The purpose of this paper is to extend the investigation of the Fleming-Viot process in discrete space started in a previous work to two specific examples. The first one corresponds to a random walk on the complete graph. Due to its…
We provide a systematic study of the notion of duality of Markov processes with respect to a function. We discuss the relation of this notion with duality with respect to a measure as studied in Markov process theory and potential theory…
Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…
We consider the problem of learning two families of time-evolving random measures from indirect observations. In the first model, the signal is a Fleming--Viot diffusion, which is reversible with respect to the law of a Dirichlet process,…
Our results characterize the long-term behavior for a broad class of $\Lambda$-Wright--Fisher processes with frequency-dependent and environmental selection. In particular, we reveal a rich variety of parameter-dependent behaviors and…
We introduce and analyze a novel type of coalescent processes called cross-multiplicative coalescent that models a system with two types of particles, $A$ and $B$. The bonds are formed only between the pairs of particles of opposite types…
We introduce a class of Markov coalescent processes on the continuous $d$-dimensional torus, in the most general setting of simultaneous multiple mergers, called the Brownian spatial coalescent. It is axiomatically defined through a…
Consider a multitype coalescent process in which each block has a colour in $\{1,\ldots,d\}$. Individual blocks may change colour, and some number of blocks of various colours may merge to form a new block of some colour. We show that if…