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.

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Author:Han Cheng Lie, Tim Sullivan
Document Type:Article
Parent Title (English):arXiv
First Page:1608.03784
Year of first publication:2016
ArXiv Id: