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

  • 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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Author:Han Cheng Lie, T. J. Sullivan
Document Type:Article
Parent Title (English):arXiv
First Page:1608.03784
Year of first publication:2016
ArXiv Id:http://arxiv.org/abs/1608.03784