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Strict positivity for stochastic heat equations

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  • Tessitore, Gianmario
  • Zabczyk, Jerzy

Abstract

The paper is concerned with the heat equation perturbed by a spatially homogeneous Wiener process. It is shown, under general conditions on the spectral density of the noise, that solutions starting from non-negative initial conditions are strictly positive for all positive times. The result has an application to the existence of a stationary solution to a stochastic Burgers equation in dimensions higher than .

Suggested Citation

  • Tessitore, Gianmario & Zabczyk, Jerzy, 1998. "Strict positivity for stochastic heat equations," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 83-98, September.
    • Handle: RePEc:eee:spapps:v:77:y:1998:i:1:p:83-98
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    References listed on IDEAS

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    1. Peszat, Szymon & Zabczyk, Jerzy, 1997. "Stochastic evolution equations with a spatially homogeneous Wiener process," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 187-204, December.
    2. Dawson, Donald A. & Salehi, Habib, 1980. "Spatially homogeneous random evolutions," Journal of Multivariate Analysis, Elsevier, vol. 10(2), pages 141-180, June.
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