Regularity of the density for a stochastic heat equation

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

2011-09-13

arxiv.org/abs/1109.2833v2

Mathematics

Probability

Scientific paper

We study the smoothness of the density of the solution to the nonlinear heat equation u_t=Lu(t,x)+\sigma(u(t,x))W on a torus with a periodic boundary condition, where L is the generator of a Levy process on the torus, and W is white noise. We use Malliavin calculus techniques to show that the law of the solution has a density with respect to the Lebesgue measure for all t >0 and x in R.

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