## 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.

Author: | Han Cheng Lie, Tim Sullivan |
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Document Type: | Article |

Parent Title (English): | arXiv |

First Page: | 1608.03784 |

Year of first publication: | 2016 |

ArXiv Id: | http://arxiv.org/abs/1608.03784 |