On large deviations of the sojourn time for an ergodic process. (English. Russian original) Zbl 0716.60025

Veretennikov, A. Yu.

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

Keywords:

stationary ergodic process; large deviation