Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables
Probability
2016-12-02 v2 Statistics Theory
Statistics Theory
Abstract
Given a sequence of Cauchy-distributed random variables defined by a sequence of location parameters and a sequence of scale parameters, we consider another sequence of random variables that is obtained by perturbing the location or scale parameter sequences. Using a result of Kakutani on equivalence of infinite product measures, we provide sufficient conditions for the equivalence of laws of the two sequences.
Keywords
Cite
@article{arxiv.1608.03784,
title = {Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables},
author = {Han Cheng Lie and T. J. Sullivan},
journal= {arXiv preprint arXiv:1608.03784},
year = {2016}
}
Comments
This paper has been withdrawn by the author because it is superseded by the article "Quasi-invariance of countable products of Cauchy measures under translations and non-unitary dilations" (arXiv:1611.10289)