Strict positivity for stochastic heat equations

Gianmario Tessitore and Jerzy Zabczyk

Stochastic Processes and their Applications, 1998, vol. 77, issue 1, 83-98

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 .

Keywords: Heat; equations; Stochastic; evolutions; Positivity (search for similar items in EconPapers)
Date: 1998
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