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Almost sure limit theorems for the maximum of a class of quasi-stationary sequences. (English) Zbl 1313.60060

Summary: This paper investigates the problem of almost sure limit theorems for the maximum of quasi-stationary sequence based on the result of K. F. Turkman and A. M. Walker [J. Appl. Probab. 20, 814–821 (1983; Zbl 0534.60036)]. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of \(D(u_k, u_n)\) and \(\alpha_{t_n,l_n}=O\left((\log \log n)^{-(1+\varepsilon)}\right)\).

MSC:

60F15 Strong limit theorems
60F05 Central limit and other weak theorems

Citations:

Zbl 0534.60036
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References:

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