Electronic Journal of Probability

Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise

Xia Chen, Yaozhong Hu, David Nualart, and Samy Tindel

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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.

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 65, 38 pp.

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

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Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes 60H07: Stochastic calculus of variations and the Malliavin calculus 60H10: Stochastic ordinary differential equations [See also 34F05] 65C30: Stochastic differential and integral equations

stochastic heat equation fractional Brownian motion Feynman-Kac formula Wiener chaos expansion intermittency

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Chen, Xia; Hu, Yaozhong; Nualart, David; Tindel, Samy. Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise. Electron. J. Probab. 22 (2017), paper no. 65, 38 pp. doi:10.1214/17-EJP83. https://projecteuclid.org/euclid.ejp/1503367245

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