Regularity of the density for the stochastic heat equation

Details Regularity of the density for the stochastic heat equation Regularity of the density for the stochastic heat equation

2007-09-17

arxiv.org/abs/0709.2663v1

Electronic J. Prob., 13, paper 74, 2248-2258, (2008)

Mathematics

Probability

Scientific paper

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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