相关论文: Feller Property and Absorption of Diffusions for M…
The Feller diffusion is studied as the limit of a coalescent point process in which the density of the node height distribution is skewed towards zero. Using a unified approach, a number of recent results pertaining to scaling limits of…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
This work focuses on a class of regime-switching jump diffusion processes with a countably infinite state space for the discrete component. Such processes can be used to model complex hybrid systems in which both structural changes, small…
In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more…
A metapopulations network is a multi-patch habitat system, where populations live and interact in the habitat patches, and individuals disperse from one patch to the other via dispersal connections. The loss of dispersal connections among…
This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance).…
We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result…
We give a substitute to Feller property for semigroups of time-changed processes; under some conditions this leads to establish sufficient (new) conditions for the semigroups to be Feller. Moreover, given a standard process and a sequence…
We use analytical methods to construct the two-parameter Feller semigroup associated with a Markov process on a line with a moving membrane such that at the points on both sides of the membrane it coincides with the ordinary diffusion…
The recent realization that entire communities fuse and separate (community coalescence) has led to a reappraisal of the forces determining species diversity and dynamics, especially in microbial communities where coalescence is likely…
We study voter models defined on large sets. Through a perspective emphasizing the martingale property of voter density processes, we prove that in general, their convergence to the Wright-Fisher diffusion only involves certain averages of…
We introduce a meta-population version of models of asymmetric exclusion models, consisting of a spatial arrangement of patches. Patches are of a specific size, indicating the maximal number of particles they can hold. We use an expansion…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
We introduce a minimal model of multilevel selection on structured populations, considering the interplay between game theory and population dynamics. Through a bottleneck process, finite groups are formed with cooperators and defectors…
Source-sink systems are metapopulations of patches that can be of variable habitat quality. They can be seen as graphs, where vertices represent the patches, and the weighted oriented edges give the probability of dispersal from one patch…
We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two…
The Wright-Fisher diffusion is a fundamentally important model of evolution encompassing genetic drift, mutation, and natural selection. Suppose you want to infer the parameters associated with these processes from an observed sample path.…
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook…
This article is concerned with a stochastic multi-patch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch…