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Regularity of the density for the stochastic heat equation

Mueller, Carl
; 
Nualart, David
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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.
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This is the published version, also available here: http://dx.doi.org/10.1214/EJP.v13-589.
Date
2008-12-18
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Volume Title
Publisher
Institute of Mathematical Statistics (IMS)
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Mathematics Scholarly Works
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NualartD_EJP_2008(13)2248.pdf
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Keywords
heat equation, white noise, Malliavin calculus, stochastic partial differential equations
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.
URI
https://hdl.handle.net/1808/17026
DOI
10.1214/EJP.v13-589
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