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- W2981069226 abstract "We consider a $phi$-mixing shift $T$ on a sequence space $Om$ and study the number $cN_N$ of returns ${ T^{q_N(n)}omin A^a_n}$ at times $q_N(n)$ to a cylinder $A^a_n$ constructed by a sequence $ainOm$ where $n$ runs either until a fixed integer $N$ or until a time $tau_N$ of the first return ${ T^{q_N(n)}omin A^b_m}$ to another cylinder $A^b_m$ constructed by $binOm$. Here $q_N(n)$ are certain functions of $n$ taking on nonnegative integer values when $n$ runs from 0 to $N$ and the dependence on $N$ is the main generalization here which requires certain conditions under which we obtain Poisson distributions limits of $cN_N$ when counting is until $N$ as $Ntoinfty$ and geometric distributions limits when counting is until $tau_N$ as $Ntoinfty$." @default.
- W2981069226 created "2019-10-25" @default.
- W2981069226 creator A5064396762 @default.
- W2981069226 date "2019-10-16" @default.
- W2981069226 modified "2023-09-27" @default.
- W2981069226 title "Limit theorems for numbers of returns in arrays under $phi$-mixing." @default.
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