37. chen.ouyang.ea:24:on#
On ergodic properties of stochastic PDEs
Le Chen, Cheng Ouyang, Samy Tindel, and Panqiu Xia
Abstract: In this note we review several situations in which stochastic PDEs exhibit ergodic properties. We begin with the basic dissipative conditions, as stated by Da Prato and Zabczyk in their classical monograph. Then we describe the singular case of SPDEs with reflection. Next we move to some degenerate (and thus more demanding) settings. Namely we recall some results obtained around 2006, concerning stochastic Navier-Stokes equations with a very degenerate noise. We finish the article by handling some cases with degenerate coefficients. This includes a new result about the parabolic Anderson model in dimension \(d \ge 3\), driven by a general class of noises and fairly general initial conditions. In this context, a phase transition is observed, expressed in terms of the noise intensity.
Keywords. Invariant measure; Dalang’s condition; ergodicity; stochastic heat equation; parabolic Anderson model; phase transition.
[COTX24] Le Chen, Cheng Ouyang, Samy Tindel & Panqiu Xia (2024) ‘On ergodic properties of stochastic PDEs’, preprint arXiv:2412.03521
@article{chen.foondun.ea:23:global,
title = {On ergodic properties of stochastic PDEs},
author = {Le Chen and Cheng Ouyang and Samy Tindel and Panqiu Xia},
year = {2024},
month = {December},
journal = {preprint arXiv:2412.03521},
url = {http://arXiv.org/abs/2412.03521}
}
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