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2017 Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise
Xia Chen, Yaozhong Hu, David Nualart, Samy Tindel
Electron. J. Probab. 22: 1-38 (2017). DOI: 10.1214/17-EJP83

Abstract

The aim of this paper is to establish the almost sure asymptotic behavior as the space variable becomes large, for the solution to the one spatial dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance structure of a fractional Brownian motion with Hurst parameter $H \in \left ( \frac 14, \frac 12 \right )$ in the space variable.

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Xia Chen. Yaozhong Hu. David Nualart. Samy Tindel. "Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise." Electron. J. Probab. 22 1 - 38, 2017. https://doi.org/10.1214/17-EJP83

Information

Received: 29 July 2016; Accepted: 16 July 2017; Published: 2017
First available in Project Euclid: 22 August 2017

zbMATH: 06797875
MathSciNet: MR3690290
Digital Object Identifier: 10.1214/17-EJP83

Subjects:
Primary: 60G15, 60H07, 60H10, 65C30

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