Simple error bounds for the multivariate Laplace approximation under weak local assumptions
Classical Analysis and ODEs
2016-04-12 v2
Abstract
The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is presented. The paper both generalizes and complements recent results by Inglot and Majerski and removes their superfluous assumption on vanishing of the third order partial derivatives of the exponent function.
Cite
@article{arxiv.1511.00302,
title = {Simple error bounds for the multivariate Laplace approximation under weak local assumptions},
author = {Piotr Majerski},
journal= {arXiv preprint arXiv:1511.00302},
year = {2016}
}
Comments
This paper gives simple and accurate error bounds for the Laplace approximation of multiple integrals under weak regularity assumptions