Electronic Journal of Probability

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

Daniel Conus, Mathew Joseph, and Davar Khoshnevisan

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465062424

Digital Object Identifier
doi:10.1214/EJP.v17-2429

Mathematical Reviews number (MathSciNet)
MR3005720

Zentralblatt MATH identifier
1296.60165

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

Keywords
The stochastic heat equation intermittency islands peaks

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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