Feynman–Kac representation of parabolic Anderson equations with general Gaussian noise

Xia Chen

doi:10.3842/umzh.v75i11.7475

Xia Chen Department of Mathematics, University of Tennessee, Knoxville, TN, USA

DOI: https://doi.org/10.3842/umzh.v75i11.7475

Keywords: Feynman-Kac formula, sub-additive process, Brownian motion

Abstract

UDC 519.21

We provide the Feynman–Kac representation for the parabolic Anderson equations driven by a general Gaussian noise. As a feature of the idea, we can mention the argument of subadditivity in establishing the required exponential integrability.

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