Hermite spatial variations for the solution to the stochastic heat equation

Héctor Araya, Johanna Garzón, Nicolás Moreno, Francisco Plaza

Abstract


In this paper, we study the Hermite spatial variations for the solution to the
stochastic heat equation with space-time white noise. We prove that these variations satisfy a central limit theorem and we obtain almost sure central limit theorem.


Keywords


Stochastic heat equation; Central limit theorem; Hermite variations; Malliavin calculus; Space-time white noise

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ISSN: 1331-0623 (Print), 1848-8013 (Online)