The Annals of Probability

Laplace's Method Revisited: Weak Convergence of Probability Measures

Chii-Ruey Hwang

Full-text: Open access

Abstract

Let $Q$ be a fixed probability on the Borel $\sigma$-field in $R^n$ and $H$ be an energy function continuous in $R^n$. A set $N$ is related to $H$ by $N = \{x \mid\inf_yH(y) = H(x)\}$. Laplace's method, which is interpreted as weak convergence of probabilities, is used to introduce a probability $P$ on $N$. The general properties of $P$ are studied. When $N$ is a union of smooth compact manifolds and $H$ satisfies some smooth conditions, $P$ can be written in terms of the intrinsic measures on the highest dimensional mainfolds in $N$.

Article information

Source
Ann. Probab., Volume 8, Number 6 (1980), 1177-1182.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994579

Digital Object Identifier
doi:10.1214/aop/1176994579

Mathematical Reviews number (MathSciNet)
MR602391

Zentralblatt MATH identifier
0452.60007

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 58C99: None of the above, but in this section

Keywords
Laplace's method smooth manifold weak convergence

Citation

Hwang, Chii-Ruey. Laplace's Method Revisited: Weak Convergence of Probability Measures. Ann. Probab. 8 (1980), no. 6, 1177--1182. doi:10.1214/aop/1176994579. https://projecteuclid.org/euclid.aop/1176994579


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