On the large-scale structure of the tall peaks for stochastic heat equations with fractional Laplacian
| Autor: | Kunwoo Kim |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Applied Mathematics Gaussian Probability (math.PR) 010102 general mathematics Mathematical analysis Structure (category theory) Hausdorff space Primary. 60H15 Secondary. 35R60 60K37 Computer Science::Computational Geometry 01 natural sciences Noise (electronics) 010104 statistics & probability symbols.namesake Modeling and Simulation FOS: Mathematics symbols Order (group theory) Heat equation 0101 mathematics Fractional Laplacian Anderson impurity model Mathematics - Probability Mathematics |
| Zdroj: | Stochastic Processes and their Applications. 129:2207-2227 |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2018.07.006 |
| Popis: | We consider stochastic heat equations with fractional Laplacian on $\mathbb{R}^d$. Here, the driving noise is generalized Gaussian which is white in time but spatially homogenous and the spatial covariance is given by the Riesz kernels. We study the large-scale structure of the tall peaks for (i) the linear stochastic heat equation and (ii) the parabolic Anderson model. We obtain the largest order of the tall peaks and compute the macroscopic Hausdorff dimensions of the tall peaks for both (i) and (ii). These results imply that both (i) and (ii) exhibit multi-fractal behavior in a macroscopic scale even though (i) is not intermittent and (ii) is intermittent. This is an extension of a recent result by Khoshnevisan et al to a wider class of stochastic heat equations. Comment: 21 pages |
| Databáze: | OpenAIRE |
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