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

Please always quote using this URN: urn:nbn:de:0297-zib-60230

- 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, T. J. Sullivan |
---|---|

Document Type: | ZIB-Report |

MSC-Classification: | 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) |

Date of first Publication: | 2016/08/23 |

Series (Serial Number): | ZIB-Report (16-40) |

ISSN: | 1438-0064 |