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Non-Gaussian scenarios for the heat equation with singular initial conditions

Author

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  • Anh, V. V.
  • Leonenko, N. N.

Abstract

Non-Gaussian limiting distributions of the rescaling solutions of the heat equation for non-Gaussian initial data with long-range dependence are discribed in terms of their multiple stochastic integral representations.

Suggested Citation

  • Anh, V. V. & Leonenko, N. N., 1999. "Non-Gaussian scenarios for the heat equation with singular initial conditions," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 91-114, November.
    • Handle: RePEc:eee:spapps:v:84:y:1999:i:1:p:91-114
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    References listed on IDEAS

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    1. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    2. Ubøe, Jan & Zhang, Tusheng, 1995. "A stability property of the stochastic heat equation," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 247-260, December.
    3. Mueller, Carl, 1998. "The heat equation with Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 67-82, May.
    4. Fox, Robert & Taqqu, Murad S., 1987. "Multiple stochastic integrals with dependent integrators," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 105-127, February.
    5. Albeverio, Sergio & Wu, Jiang-Lun & Zhang, Tu-Sheng, 1998. "Parabolic SPDEs driven by Poisson white noise," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 21-36, May.
    6. Terdik, György, 1992. "Stationarity in fourth order and the marginal bispectrum for bilinear models with Gaussian residuals," Stochastic Processes and their Applications, Elsevier, vol. 42(2), pages 315-327, September.
    7. Leonenko, N. N. & Woyczynski, W. A., 1998. "Exact parabolic asymptotics for singular -D Burgers' random fields: Gaussian approximation," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 141-165, August.
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    Cited by:

    1. Anh, V. V. & Leonenko, N. N., 2000. "Scaling laws for fractional diffusion-wave equations with singular data," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 239-252, July.
    2. N. N. Leonenko & M. D. Ruiz-Medina, 2008. "Gaussian Scenario for the Heat Equation with Quadratic Potential and Weakly Dependent Data with Applications," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 595-620, December.

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