Let $\mathbf{X} = \{X_k\}$ be an i.i.d. real random sequence, let $\epsilon = \{\epsilon_k\}$ be a Rademacher sequence independent of $\mathbf{X}$ and let $\mathbf{a} = \{a_k\}$ be a deterministic real sequence. The aim of this paper is to prove that the mutual absolute continuity of probability measures induced by $\{X_k\}$ and $\{X_k + a_k\epsilon_k\}$ implies $\mathbf{a} \in \ell_4$. This is a generalization of a result of Shepp.
Publié le : 1994-04-14
Classification:
Absolute continuity of infinite product measures,
random translation,
Rademacher sequence,
60G30,
28C20
@article{1176988742,
author = {Okazaki, Yoshiaki and Sato, Hiroshi},
title = {Distinguishing a Sequence of Random Variables from a Random Translate of Itself},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 1092-1096},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988742}
}
Okazaki, Yoshiaki; Sato, Hiroshi. Distinguishing a Sequence of Random Variables from a Random Translate of Itself. Ann. Probab., Tome 22 (1994) no. 4, pp. 1092-1096. http://gdmltest.u-ga.fr/item/1176988742/