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2012 Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs
Daniel Conus, Mathew Joseph, Davar Khoshnevisan
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Electron. J. Probab. 17: 1-15 (2012). DOI: 10.1214/EJP.v17-2429

Abstract

We consider the nonlinear stochastic heat equation in one dimension. Under some conditions on the nonlinearity, we show that the "peaks" of the solution are rare, almost fractal like. We also provide an upper bound on the length of the "islands", the regions of large values. These results are obtained by analyzing the correlation length of the solution.

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Daniel Conus. Mathew Joseph. Davar Khoshnevisan. "Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs." Electron. J. Probab. 17 1 - 15, 2012. https://doi.org/10.1214/EJP.v17-2429

Information

Accepted: 8 December 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1296.60165
MathSciNet: MR3005720
Digital Object Identifier: 10.1214/EJP.v17-2429

Subjects:
Primary: 60H15
Secondary: 35R60

Keywords: Intermittency , islands , peaks , The stochastic heat equation

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