Exact asymptotics of Laplace integrals on nonsmooth functions.
type: Item
instance of: scholarly article
title: Exact asymptotics of Laplace integrals on nonsmooth functions.
zbMATH Open document ID: 1066.41029
DOI: 10.1023/A:1024006031243
author: E. I. Ostrovskij
published in: Mathematical Notes
publication date: 2004-12-02T00:00:00Z
review text: The author determines the exact asymptotics (including estimates for the remainder term) of the Laplace type integral \[ I(\lambda)=\int_X g(x) \exp(\lambda S(x))\,\mu(dx) \quad \text{ as } \lambda \to \infty\,. \] Here \((X,B;\mu)\) is a finite measure space, and \(g\) and \(S\) are real valued measurable functions such that \[ \text{ess sup}_{x\in X} S(x) < \infty, \quad \text{ess sup}_{x\in X} | g(x)| < \infty, \quad \mu\{x\in X: g(x)=0\}=0\,. \] In particular, no assumptions on the topological structure of \(X\) are made, and no smoothness conditions on \(g\) and \(S\) are posed. Some concrete examples and an application to probability theory are given.
reviewed by: Thomas Kühn
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 60E10
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 2120998
zbMATH Keywords: Laplace integral
zbMATH Keywords: asymptotics of Laplace integral
zbMATH Keywords: nonsmooth function
zbMATH Keywords: measure space
zbMATH Keywords: Lebesgue integral
MaRDI profile type: Publication
full work available at URL: a:1024006031243
OpenAlex ID: W30944961
Recommended article: Asymptotic estimates for Laplace integrals
Recommended article: Asymptotics of Laplace-Dirichlet integrals
Recommended article: Asymptotical behavior of Laplace-Stieltjes integrals.
Recommended article: Exact asymptotics of Laplace-type Wiener integrals for $ L^p$-functionals
Recommended article: Asymptotic integration of differential equations with singular \(p\)-Laplacian.
Recommended article: Q3541644
Recommended article: Q3219282
Recommended article: Q4300792
Recommended article: Higher asymptotics of Laplace's approximation
Recommended article: Asymptotic integration of nonlinear \(\phi\)-Laplacian differential equations
description: scientific article; zbMATH DE number 2120998