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- W61943105 abstract "Consider a stationary stochastic process X 1, ..., X 1. We study the distribution law of the number of occurrences of a string of symbols in this process. We consider three different ways to compute it. 1) When the string is the first block generated by the process, called N t . 2) When the string is the first block generated by an independent, copy of the process, called M t . 3) When the string ( underset{raise0.3emhbox{$smash{scriptscriptstylethicksim}$}}{a} ) is previously fixed, called N t (( underset{raise0.3emhbox{$smash{scriptscriptstylethicksim}$}}{a} )). We show how this laws can be approximated by a Poisson law with an explicit error for each approximation. We then derive approximations for the distribution of the first occurrence time of the string, according also to the above three different ways to chose it. The base of the proofs is the Chen-Stein method which is commonly used to prove approximations in total variation distance in the Markov context. We show how to apply it in non-Markovian mixing processes." @default.
- W61943105 created "2016-06-24" @default.
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- W61943105 date "2008-01-01" @default.
- W61943105 modified "2023-10-01" @default.
- W61943105 title "Poisson Approximations via Chen-Stein for Non-Markov Processes" @default.
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- W61943105 doi "https://doi.org/10.1007/978-3-7643-8786-0_1" @default.
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