The Annals of Probability

Fisher Information and Detection of a Euclidean Perturbation of an Independent Stationary Process

J. Michael Steele

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Abstract

An independent stationary process $\{X_i\}^\infty_{i=1}$ in $\mathbb{R}^n$ is perturbed by a sequence of Euclidean motions to obtain a new process $\{Y_i\}^\infty_{i=1}$. Criteria are given for the singularity or equivalence of these processes. When the distribution of the $X$ process has finite Fisher information, the criteria are necessary and sufficient. Moreover, it is proved that it is exactly under the condition of finite Fisher information that the criteria are necessary and sufficient.

Article information

Source
Ann. Probab., Volume 14, Number 1 (1986), 326-335.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992631

Digital Object Identifier
doi:10.1214/aop/1176992631

Mathematical Reviews number (MathSciNet)
MR815974

Zentralblatt MATH identifier
0592.60033

JSTOR
links.jstor.org

Subjects
Primary: 60G30: Continuity and singularity of induced measures
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization

Keywords
Fisher information Kakutani's product theorem product measures Euclidean motions singular processes Hellinger integrals

Citation

Steele, J. Michael. Fisher Information and Detection of a Euclidean Perturbation of an Independent Stationary Process. Ann. Probab. 14 (1986), no. 1, 326--335. doi:10.1214/aop/1176992631. https://projecteuclid.org/euclid.aop/1176992631


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