Electronic Communications in Probability

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

Yaozhong Hu, Jingyu Huang, and David Nualart

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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 $\mathbb{R} ^d$. 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.

Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 21, 13 pp.

Dates
Received: 15 June 2015
Accepted: 27 January 2016
First available in Project Euclid: 1 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456840982

Digital Object Identifier
doi:10.1214/16-ECP4364

Mathematical Reviews number (MathSciNet)
MR3485390

Zentralblatt MATH identifier
1338.60158

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
stochastic heat equation Feynman-Kac formula intermittency front Malliavin calculus comparison principle

Rights
Creative Commons Attribution 4.0 International License.

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


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References

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