11. chen.hu.ea:17:two-point#
Two-point correlation function and Feynman-Kac formula for the stochastic heat equation
Le Chen, Yaozhong Hu, David Nualart
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 [CD15b] 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.
MSC 2010 subject classifications: Primary 60H15. Secondary 60G60, 35R60.
Keywords: stochastic heat equation, two-point correlation function, Feynman-Kac formula, Brownian local time, Malliavin calculus.
[CHN17] Chen, Le, Hu, Yaozhong & Nualart, David (2017) ‘Two-point correlation function and Feynman-Kac formula for the stochastic heat equation’, Potential Anal. 46, 779–797. <https://doi.org/10.1007/s11118-016-9601-y>
@article{chen.hu.ea:17:two-point,
author = {Chen, Le and Hu, Yaozhong and Nualart, David},
title = {Two-point correlation function and {F}eynman-{K}ac formula for the stochastic heat equation},
journal = {Potential Anal.},
fjournal = {Potential Analysis. An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis},
volume = {46},
year = {2017},
number = {4},
pages = {779--797},
issn = {0926-2601},
mrclass = {60H15 (35K15 35R60 60G60 60H07 60J55)},
mrnumber = {3636598},
mrreviewer = {Robert C. Dalang},
doi = {10.1007/s11118-016-9601-y},
url = {https://doi.org/10.1007/s11118-016-9601-y}
}
References: Airault et al. [ARZ00]; Albeverio et al. [ABD95]; Albeverio et al. [AGHKH05]; Bertini and Cancrini [BC98]; Carmona and Molchanov [CM94]; Chen and Dalang [CD15b]; Chen and Kim [CK17]; Chung and Williams [CW90]; Erdélyi et al. [EMOT81b]; Hu and Nualart [HN09]; Nualart [Nua06]; Nualart and Vives [NV94]; Revuz and Yor [RY99];