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On the large-scale structure of the tall peaks for stochastic heat equations with fractional Laplacian

Title
On the large-scale structure of the tall peaks for stochastic heat equations with fractional Laplacian
Authors
Kim, K.
Date Issued
Jun-2019
Publisher
ELSEVIER SCIENCE BV
Abstract
Consider stochastic heat equations with fractional Laplacian on R-d. The driving noise is generalized Gaussian which is white in time but spatially homogeneous. 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 peaks and compute the macroscopic Hausdorff dimensions of the peaks for (i) and (ii). These result imply that both (i) and (ii) exhibit multi-fractal behavior even though only (ii) is intermittent. This is an extension of a result of Khoshnevisan et al. (2017) to a wider class of stochastic heat equations. (C) 2018 Elsevier B.V. All rights reserved.
URI
http://oasis.postech.ac.kr/handle/2014.oak/99876
ISSN
0304-4149
Article Type
Article
Citation
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 129, no. 6, page. 2207 - 2227, 2019-06
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 KIM, KUNWOO
Dept of Mathematics
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