Dear colleagues,
We are happy to announce the following online talk:
Speaker: Guangqu Zheng (University of Kansas)
Title: Malliavin derivatives of hyperbolic Anderson model with applications to its absolute continuity and spatial averages.
Date and time: Monday May 10, 17:30-18:30 (Rome time zone)
Abstract: see below.
Meeting ID: 838 4386 4962
Passcode: 5gVVXb
This talk is the second of the
(PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics
organized
jointly by the universities Milano-Bicocca, Pavia, Milano-Politecnico
and Milano-Statale.
Participation is free and welcome! (though limited to 100 participants for technical reasons)
Best regards
The organizers (Mario Maurelli, Carlo Orrieri, Maurizia Rossi, Margherita Zanella)
Abstract: In this talk, we present recent work on the hyperbolic
Anderson model driven by a space-time colored Gaussian homogeneous noise
with spatial dimension one and two. Under mild assumptions, we provide
Lp-estimates of the iterated Malliavin derivatives of the solution in
terms of the fundamental solution of the wave solution. We present two
applications:
(1) We present quantitative central limit theorems for spatial averages
of the solution to the hyperbolic Anderson model, where the rates of
convergence are described by the total variation distance. These
quantitative results have been elusive so far due to the temporal
correlation of the noise blocking us from using the Itô calculus.
(2) We establish the absolute continuity of the law for the hyperbolic
Anderson model. The Lp-estimates of Malliavin derivatives are crucial
ingredients to verify a local version of Bouleau-Hirsch criterion for
absolute continuity. Our approach substantially simplifies the arguments
for the one-dimensional case, which has been studied in the recent work
by Balan, Quer-Sardanyons and Song (2019).
This talk is based on the joint work (arXiv:2101.10957) with R. Balan, D. Nualart and L. Quer-Sardanyons (2021).