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- W1982518868 abstract "Given a periodic point ${itomega}$ in a ${itpsi}$ -mixing shift with countable alphabet, the sequence ${S_{n}}$ of random variables counting the number of multiple returns in shrinking cylindrical neighborhoods of ${itomega}$ is considered. Necessary and sufficient conditions for the convergence in distribution of ${S_{n}}$ are obtained, and it is shown that the limit is a Pólya–Aeppli distribution. A global condition on the shift system which guarantees the convergence in distribution of ${S_{n}}$ for every periodic point is introduced. This condition is used to derive results for $f$ -expansions and Gibbs measures. Results are also obtained concerning the possible limit distribution of sub-sequences ${S_{n_{k}}}$ . A family of examples in which there is no convergence is presented. We also exhibit an example for which the limit distribution is pure Poissonian." @default.
- W1982518868 created "2016-06-24" @default.
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- W1982518868 date "2015-02-11" @default.
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- W1982518868 title "Compound Poisson statistics for multiple returns in shrinking cylinders for mixing processes" @default.
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- W1982518868 doi "https://doi.org/10.1017/etds.2014.139" @default.
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