Random fields and random sampling. (English) Zbl 1463.60071

The authors study the limit in distribution of the maximum of a stationary bivariate real random field, sampled at double random times under some dependence conditions. It is shown that the limit distribution is a max-semistable distribution when the random samples have a geometric growth pattern. When the random field is sampled at double random times, it is shown that the limit in distribution is a mixture distribution. The results are extensions of the results in [the second author and L. Canto e Castro, Theory Probab. Appl. 47, No. 2, 365–374 (2002) and Teor. Veroyatn. Primen. 47, No. 2, 402–410 (2002; Zbl 1037.60050); H. Choi, Central limit theory and extremes of random fields. Chapel Hill, NC: University of North Carolina (PhD Thesis) (2001); A. Freitas et al., Test 21, No. 1, 116–131 (2012; Zbl 1266.60094)].


60G60 Random fields
60G70 Extreme value theory; extremal stochastic processes
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