对称 Cauchy 分布随机变量序列的 Cameron-Martin 定理
概率论
2016-12-02 v2 统计理论
统计理论
摘要
给定由位置参数序列和尺度参数序列定义的 Cauchy 分布随机变量序列，我们考虑通过扰动位置或尺度参数序列得到的另一随机变量序列。利用 Kakutani 关于无穷乘积测度等价性的结果，我们给出了两个序列定律等价的充分条件。
引用
@article{arxiv.1608.03784,
title = {Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables},
author = {Han Cheng Lie and T. J. Sullivan},
journal= {arXiv preprint arXiv:1608.03784},
year = {2016}
}
备注
This paper has been withdrawn by the author because it is superseded by the article "Quasi-invariance of countable products of Cauchy measures under translations and non-unitary dilations" (arXiv:1611.10289)