The Annals of Probability

An Extended Dichotomy Theorem for Sequences of Pairs of Gaussian Measures

G. K. Eagleson

Full-text: Open access

Abstract

A dichotomy for sequences of pairs of Gaussian measures is proved. This result is then used to give a simple proof of the famous equivalence/singularity dichotomy for Gaussian processes. The proof uses tightness arguments and can be directly applied to the theory of hypothesis testing to show that two sequences of simple hypotheses which specify Gaussian measures are either contiguous or entirely separable.

Article information

Source
Ann. Probab., Volume 9, Number 3 (1981), 453-459.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994417

Digital Object Identifier
doi:10.1214/aop/1176994417

Mathematical Reviews number (MathSciNet)
MR614629

Zentralblatt MATH identifier
0462.60042

JSTOR
links.jstor.org

Subjects
Primary: 60G30: Continuity and singularity of induced measures
Secondary: 62F03: Hypothesis testing

Keywords
Absolute continuity Gaussian processes contiguity

Citation

Eagleson, G. K. An Extended Dichotomy Theorem for Sequences of Pairs of Gaussian Measures. Ann. Probab. 9 (1981), no. 3, 453--459. doi:10.1214/aop/1176994417. https://projecteuclid.org/euclid.aop/1176994417


Export citation