Sharp errors for point-wise Poisson approximations in mixing processes
Sharp errors for point-wise Poisson approximations in mixing processes
复制标题
混合过程中逐点泊松近似的尖锐误差
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
N. Vergne
中科院分区：
文献类型：
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作者：
M. Abadi;N. Vergne
我们描述了一个随机过程中的符号串的出现次数的统计：采取一个字符串A的长度为n，我们证明了访问A的次数到时间t，表示为Nt，有近似泊松分布。我们提供了一个尖锐的错误，这种近似。与以前的作品，提出统一的误差项的基础上的总变化距离，我们的错误是逐点的。作为副产品，我们得到Nt的所有矩都是有限的。此外，我们获得了所有这些显式的近似。我们的结果适用于验证了非线性混合条件的过程.误差项被明确地表示为速率函数的函数，并且易于计算。
We describe the statistics of the number of occurrences of a string of symbols in a stochastic process: taking a string A of length n, we prove that the number of visits to A up to time t, denoted by Nt, has approximately a Poisson distribution. We provide a sharp error for this approximation. In contrast to previous works which present uniform error terms based on the total variation distance, our error is point-wise. As a byproduct we obtain that all the moments of Nt are finite. Moreover, we obtain explicit approximations for all of them. Our result holds for processes that verify the ϕ-mixing condition. The error term is explicitly expressed as a function of the rate function ϕ and is easily computable.