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On the intermittency front of stochastic heat equation driven by colored noises

Hu, Yaozhong
; 
Huang, Jingyu
; 
Nualart, David
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Abstract
We study the propagation of high peaks (intermittency fronts) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in RdRd. The noise is assumed to have a general homogeneous covariance in both time and space, and the solution is interpreted in the senses of the Wick product. We give some estimates for the upper and lower bounds of the propagation speed, based on a moment formula of the solution. When the space covariance is given by a Riesz kernel, we give more precise bounds for the propagation speed.
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Date
2016-03-01
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Institute of Mathematical Statistics
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Mathematics Scholarly Works
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Hu_IMS_2016.pdf
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Keywords
Stochastic heat equation, Feynman-Kac formula, Intermittency front, Malliavin calculus, Comparison principle
Citation
Hu, Yaozhong; Huang, Jingyu; Nualart, David. On the intermittency front of stochastic heat equation driven by colored noises. Electron. Commun. Probab. 21 (2016), paper no. 21, 13 pp. doi:10.1214/16-ECP4364. https://projecteuclid.org/euclid.ecp/1456840982
URI
https://hdl.handle.net/1808/25321
DOI
10.1214/16-ECP4364
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