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Two-point Correlation Function and Feynman-Kac Formula for the Stochastic Heat Equation

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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 Chen and Dalang (Ann. Probab. 2015) 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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Authors and Affiliations

  1. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA

    Le Chen, Yaozhong Hu & David Nualart

Authors
  1. Le Chen
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  2. Yaozhong Hu
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  3. David Nualart
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Correspondence to Le Chen.

Additional information

Research partially supported by a fellowship from Swiss National Science Foundation (P2ELP2_151796)

Research partially supported by a grant from the Simons Foundation #209206

Research partially supported by the NSF grant DMS1512891 and the ARO grant FED0070445

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Chen, L., Hu, Y. & Nualart, D. Two-point Correlation Function and Feynman-Kac Formula for the Stochastic Heat Equation. Potential Anal 46, 779–797 (2017). https://doi.org/10.1007/s11118-016-9601-y

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  • DOI: https://doi.org/10.1007/s11118-016-9601-y

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