8 papers
Correction to "The stepping stone model in a random environment" -- limit theorems for the occupation time and intersection time of reversible random walks in random environments
Raphaël Forien
This note corrects a mistake in the author's above-mentionned published work regarding the intersection local time of two independent random walks in a random environment. The rand…
Stochastic epidemic model with varying infectivity and waning immunity: the law of large numbers with unbounded infectivity
Raphaël Forien, Ãtienne Pardoux
We revisit the large population limit of our epidemic model with infection age dependent infectivity and progressive immunity waning, under the assumption that the supremum in …
Fluctuations for fully pushed stochastic fronts
Alison Etheridge, Raphaël Forien, Thomas Hughes +1
We study the asymptotic behaviour, in the small noise limit, of stochastic travelling wave solutions to reaction-diffusion equations perturbed by Wright-Fisher noise. Such equation…
Stochastic neutral fractions and the effective population size
Raphaël Forien, Emmanuel Schertzer, Zsófia Talyigás +1
The dynamics of a general structured population is modelled using a general stochastic differential equation (SDE) with an infinite decomposability property. This property allows t…
Central limit theorems describing isolation by distance under various forms of power-law dispersal
Raphaël Forien, Bastian Wiederhold
In this paper, we uncover new asymptotic isolation by distance patterns occurring under long-range dispersal of offspring. We extend a recent work of the first author, in which thi…
Stochastic epidemic models with varying infectivity and waning immunity
Raphaël Forien, Guodong Pang, Ãtienne Pardoux +1
We study an individual-based stochastic epidemic model in which infected individuals become susceptible again following each infection. In contrast to classical compartment models,…