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9 papers · 2 filters
Population processes with unbounded extinction rate conditioned to non-extinction
Nicolas Champagnat, Denis Villemonais
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes an…
One-dimensional reflected rough differential equations
Aurelien Deya, Massimiliano Gubinelli, Martina Hofmanova +1
We prove existence and uniqueness of the solution of a one-dimensional rough differential equation driven by a step-2 rough path and reflected at zero. In order to deal with the la…
Initial-Boundary Value Problem for the heat equation - A stochastic algorithm
Madalina Deaconu, Samuel Herrmann
The Initial-Boundary Value Problem for the heat equation is solved by using a new algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalizati…
The critical Galton-Watson process vanishes
Olivier Garet
The Galton-Watson process belongs to standard teaching in probability. The basic theorem says that survival is only possible when the fecondity exceeds 1. The classical proof is es…
Gaussian approximations for chemostat models in finite and infinite dimensions
Bertrand Cloez, Coralie Fritsch
In a chemostat, bacteria live in a growth container of constant volume in which liquid is injected continuously. Recently, Campillo and Fritsch introduced a mass-structured individ…
Stretch Factor of Long Paths in a planar Poisson-Delaunay Triangulation
Nicolas Chenavier, Olivier Devillers
Let , where is a planar Poisson point process of intensity . We provide a first non-trivial lower bound for the distance between the expected le…