REAL

A landscape of peaks: The intermittency islands of the stochastic heat equation with Lévy noise

Chong, Carsten and Kevei, Péter (2023) A landscape of peaks: The intermittency islands of the stochastic heat equation with Lévy noise. ANNALS OF PROBABILITY, 51 (4). pp. 1449-1501. ISSN 0091-1798

[img] Text
islands_mult_arxiv.pdf
Restricted to Repository staff only

Download (506kB)

Abstract

We show that the spatial profile of the solution to the stochastic heat equation features multiple layers of intermittency islands if the driving noise is non-Gaussian. On the one hand, as expected, if the noise is sufficiently heavy-tailed, the largest peaks of the solution will be taller under multiplicative than under additive noise. On the other hand, surprisingly, as soon as the noise has a finite moment of order 2d, where d is the spatial dimension, the largest peaks will be of the same order for both additive and multiplicative noise, which is in sharp contrast to the behavior of the solution under Gaussian noise. However, in this case a closer inspection reveals a second layer of peaks, beneath the largest peaks, that is exclusive to multiplicative noise and that can be observed by sampling the solution on the lattice. Finally, we compute the macroscopic Hausdorff and Minkowski dimensions of the intermittency islands of the solution. Under both additive and multiplicative noise, if it is not too heavy-tailed, the largest peaks will be self-similar in terms of their large-scale multifractal behavior. But under multiplicative noise, this type of self-similarity is not present in the peaks observed on the lattice.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika
Depositing User: Peter Kevei
Date Deposited: 25 Sep 2023 12:34
Last Modified: 25 Sep 2023 12:34
URI: http://real.mtak.hu/id/eprint/174749

Actions (login required)

Edit Item Edit Item