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On large deviations of the sojourn time for an ergodic process. (English. Russian original) Zbl 0716.60025
Theory Probab. Appl. 35, No. 2, 390-393 (1990); translation from Teor. Veroyatn. Primen. 35, No. 2, 340-343 (1990).
Let \(X_ n\in (E,{\mathcal B})\), \(-\infty <n<\infty\), be a stationary ergodic process, where (E,\({\mathcal B})\) be a Polish space, \[ L_ n(\Gamma)=n^{-1}\sum^{n-1}_{k=0}I(X_ k\in \Gamma),\quad n>0,\quad \Gamma \in {\mathcal B}, \] \(Q_ n\) be a low distribution of \(L_ n\). The asymptotic of a large deviation of \(Q_ n\) is investigated.
Reviewer: N.Leonenko

MSC:
60F10 Large deviations
60G10 Stationary stochastic processes
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