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arXiv · 1109.2833

Regularity of the density for a stochastic heat equation

Pejman Mahboubi
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Abstract

We study the smoothness of the density of the solution to the nonlinear heat equation u_t=Lu(t,x)+σ(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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Pejman Mahboubi. 2011-09-14. Regularity of the density for a stochastic heat equation. https://arxiv.org/abs/1109.2833

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