Related papers: The reversibility and an SPDE for the generalized …
Let $\Lambda$ be a finite measure on the unit interval. A $\Lambda$-Fleming-Viot process is a probability measure valued Markov process which is dual to a coalescent with multiple collisions ($\Lambda$-coalescent) in analogy to the duality…
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…
Reversibility of the Fleming-Viot process with mutation, selection, and recombination is well understood. In this paper, we study the reversibility of a system of Fleming-Viot processes that live on a countable number of colonies…
For a probability-measure-valued neutral Fleming-Viot process $Z_t$ with L\'evy mutation and resampling mechanism associated to a general $\Lambda$-coalescent with multiple collisions, we prove the instantaneous propagation of supports.…
Reversible measures of the Fleming-Viot process are shown to be characterized as quasi-invariant measures with a cocycle given in terms of the mutation operator. As applications, we give certain integral characterization of…
The generalized Fleming-Viot processes were defined in 1999 by Donnelly and Kurtz using a particle model and by Bertoin and Le Gall in 2003 using stochastic flows of bridges. In both methods, the key argument used to characterize these…
If $\mathbf Y$ is a standard Fleming-Viot process with constant mutation rate (in the infinitely many sites model) then it is well known that for each $t>0$ the measure $\mathbf Y_t$ is purely atomic with infinitely many atoms. However,…
We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot processes, which describe the evolution of a…
The d-dimensional Lambda-Fleming-Viot generator acting on functions g(x), with x being a vector of d allele frequencies, can be written as a Wright-Fisher generator acting on functions g with a modified random linear argument of x induced…
Coalescents with multiple collisions (also called Lambda-coalescents or simple exchangeable coalescents) are used as models of genealogies. We study a new class of Markovian coalescent processes connected to a population model with…
We consider the tree-valued Fleming-Viot process, $(\mathcal X_t)_{t\geq 0}$, with mutation and selection as studied in Depperschmidt, Greven, Pfaffelhuber (2012). This process models the stochastic evolution of the genealogies and…
The star-shaped $\Lambda$-coalescent and corresponding $\Lambda$-Fleming-Viot process where the $\Lambda$ measure has a single atom at unity are studied in this paper. The transition functions and stationary distribution of the…
Consider a system $X = ((x_\xi(t)), \xi \in \Omega_N)_{t \geq 0}$ of interacting Fleming-Viot diffusions with mutation and selection which is a strong Markov process with continuous paths and state space $(\CP(\I))^{\Omega_N}$, where $\I$…
This article presents a variant of Fleming-Viot particle systems, which are a standard way to approximate the law of a Markov process with killing as well as related quantities. Classical Fleming-Viot particle systems proceed by simulating…
This paper provides a construction of a Fleming--Viot measure valued diffusion process, for which the transition function is known, by extending recent ideas of the Gibbs sampler based Markov processes. In particular, we concentrate on the…
We study the long-time convergence of a Fleming-Viot process, in the case where the underlying process is a metastable diffusion killed when it reaches some level set. Through a coupling argument, we establish the long-time convergence of…
Kingman derived the Ewens sampling formula for random partitions from the genealogy model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process. M\"ohle described the recursion which…
Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process, and…
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…
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…