## Abstract

Let {*X*
_{
n
}} be a stationary sequence and {*k*
_{
n
}} be a nondecreasing sequence such that *k*
_{
n+1}/*k*
_{
n
}→*r*≥1. Assume that the limit distribution *G* of \(M_{k_{n}}\) with an appropriate linear normalization exists. We consider the maxima *M*
_{
n
}=max {*X*
_{
i
},*i*≤*n*} sampled at random times *T*
_{
n
}, where *T*
_{
n
}/*k*
_{
n
} converges in probability to a positive random variable *D*, and show that the limit distribution of \(M_{T_{n}}\) exists under weak mixing conditions. The limit distribution of \(M_{T_{n}}\) is a mixture of *G* and the distribution of *D*.

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Freitas, A., Hüsler, J. & Temido, M.G. Limit laws for maxima of a stationary random sequence with random sample size.
*TEST* **21**, 116–131 (2012). https://doi.org/10.1007/s11749-011-0238-2

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DOI: https://doi.org/10.1007/s11749-011-0238-2