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Cameron-Martin theorems for sequences of symmetric 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.

preprint2016arXivOpen access
Han Cheng LieT. J. Sullivan
math.PRmath.STStatistics Theory
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Han Cheng LieT. J. Sullivan

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