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.
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