Electronic Journal of Probability

Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs

Daniel Conus, Mathew Joseph, and Davar Khoshnevisan

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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.

Article information

Electron. J. Probab., Volume 17 (2012), paper no. 102, 15 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]

The stochastic heat equation intermittency islands peaks

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Conus, Daniel; Joseph, Mathew; Khoshnevisan, Davar. Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs. Electron. J. Probab. 17 (2012), paper no. 102, 15 pp. doi:10.1214/EJP.v17-2429. https://projecteuclid.org/euclid.ejp/1465062424

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