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arXiv · 1509.01121

Two-point correlation function and Feynman-Kac formula for the stochastic heat equation

Le Chen·Yaozhong Hu·David Nualart
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Abstract

In this paper, we obtain an explicit formula for the two-point correlation function for the solutions to the stochastic heat equation on $\mathbb{R}$. The bounds for $p$-th moments proved in [3] are simplified. We validate the Feynman-Kac formula for the $p$-point correlation function of the solutions to this equation with measure-valued initial data.

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Le Chen, Yaozhong Hu, David Nualart. 2015-09-03. Two-point correlation function and Feynman-Kac formula for the stochastic heat equation. https://arxiv.org/abs/1509.01121

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