Regularity of the density for the stochastic heat equation

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Issue Date
2008-12-18Author
Mueller, Carl
Nualart, David
Publisher
Institute of Mathematical Statistics (IMS)
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
Show full item recordAbstract
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.
Description
This is the published version, also available here: http://dx.doi.org/10.1214/EJP.v13-589.
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Citation
Mueller, Carl & Nualart, David. "Regularity of the density for the stochastic heat equation." Electronic Journal of Probability Vol. 13 (2008), Paper no. 74, pages 2248–2258. http://dx.doi.org/10.1214/EJP.v13-589.
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