## Electronic Communications in Probability

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

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

Yaozhong Hu, Jingyu Huang, and David Nualart

#### 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