The constant coefficient in precise Laplace asymptotics for gPAM
Abstract
This article resumes the analysis of precise Laplace asymptotics for the generalised Parabolic Anderson Model (gPAM) initiated by Peter Friz and the author. More precisely, we provide an explicit formula for the constant coefficient in the asymptotic expansion in terms of traces and Carleman-Fredholm determinants of certain explicit operators. The proof combines classical Gaussian analysis in abstract Wiener spaces with arguments from the theory of regularity structures. As an ingredient, we prove that the minimiser in the (extended) phase functional of gPAM has better than just Cameron-Martin regularity.
Keywords
Cite
@article{arxiv.2202.03358,
title = {The constant coefficient in precise Laplace asymptotics for gPAM},
author = {Tom Klose},
journal= {arXiv preprint arXiv:2202.03358},
year = {2024}
}
Comments
40 pages, incl. references. Final version to appear in Annales de l'Institut Henri Poincar\'e (B) Probabilit\'es et Statistiques. A mistake in an earlier version has been fixed and the presentation and formatting have been improved