Regularity of the density for a stochastic heat equation

2011/09/13 by Pejman Mahboubi, Mahboubi, Pejman
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1109.2833

openalex publication_date 2011/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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