Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables
arXiv:1608.03784
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.
This paper has been withdrawn by the author because it is superseded by the article "Quasi-invariance of countable products of Cauchy measures under translations and non-unitary dilations" (arXiv:1611.10289)