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Distributions stationnaires attractives pour l'équation de la chaleur stochastique — Attracting Stationary Distributions for the Semi-Discrete Stochastic Heat Equation

23rd September 2019   -   4th October 2019
CIRM Luminy, France


We consider the semidiscrete stochastic heat equation on the lattice Z d , d ≥ 3, with a small noise term that is white in time. The goal of this project is to show that the equation admits a global solution whose distribution attracts solutions with initial conditions in a certain class, both in the forward and in the pullback sense. Determining how broad this class of initial conditions can be is one important aspect.