Intermittency for the Hyperbolic Anderson Model with rough noise in space

Raluca M. Balan, Maria Jolis and Lluís Quer-Sardanyons

Stochastic Processes and their Applications, 2017, vol. 127, issue 7, 2316-2338

Abstract: In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst index H∈(14,12). Initial data are assumed to be constant. First, we prove that this equation has a unique solution (in the Skorohod sense) and obtain an exponential upper bound for the p-th moment the solution, for any p≥2. Condition H>14 turns out to be necessary for the existence of solution. Secondly, we show that this solution coincides with the one obtained by the authors in a recent publication, in which the solution is interpreted in the Itô sense. Finally, we prove that the solution of the equation in the Skorohod sense is weakly intermittent.

Keywords: Stochastic partial differential equations; Malliavin calculus; Stochastic wave equation; Intermittency (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:7:p:2316-2338

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DOI: 10.1016/j.spa.2016.10.009

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