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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 74 open journal systems 


Regularity of the density for the stochastic heat equation

Carl E Mueller, University of Rochester
David Nualart, University of Kansas


Abstract
We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise. Using Malliavin calculus, we reduce the problem to a question of negative moments of solutions of a linear heat equation with multiplicative white noise. Then we settle this question by proving that solutions to the linear equation have negative moments of all orders.


Full text: PDF

Pages: 2248-2258

Published on: December 21, 2008
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Electronic Journal of Probability. ISSN: 1083-6489