Probability Seminar

Spatial ergodicity and quantitative central limit theorems for the stochastic heat equation

Speaker(s): David Nualart
In this lecture we will present some results on the asymptotic behavior of spatial averages over large blocks of the stochastic heat equation driven by a Gaussian noise which is white in time and it has an homogeneous spatial covariance. We will discuss the spatial ergodicity, that can be established using Poincaré’s inequality and quantitative central limit theorems for spatial averages. The goal is to show a rate of convergence in total variation distance, by means of a combination of Malliavin calculus techniques and Stein’s method for normal approximations.

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