Electronic Journal of Probability
- Electron. J. Probab.
- Volume 17 (2012), paper no. 102, 15 pp.
Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs
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.
Electron. J. Probab., Volume 17 (2012), paper no. 102, 15 pp.
Accepted: 8 December 2012
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
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]
This work is licensed under aCreative Commons Attribution 3.0 License.
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