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arXiv · 1608.03784

Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables

Han Cheng Lie·T. J. Sullivan
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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.

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Han Cheng Lie, T. J. Sullivan. 2016-08-12. Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables. https://arxiv.org/abs/1608.03784

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