## The Annals of Probability

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

J. Michael Steele

#### 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

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