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16 papers · 2 filters
On stochastic calculus with respect to q-Brownian motion
Aurélien Deya, René Schott
Following the approach and the terminology introduced in [A. Deya and R. Schott, On the rough paths approach to non-commutative stochastic calculus, J. Funct. Anal., 2013], we cons…
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…
Uniform convergence to the Q-process
Nicolas Champagnat, Denis Villemonais
The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribut…
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…