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Random fields and random sampling

Sandra Dias, Maria da Graça Temido (2019)

Kybernetika

We study the limiting distribution of the maximum value of a stationary bivariate real random field satisfying suitable weak mixing conditions. In the first part, when the double dimensions of the random samples have a geometric growing pattern, a max-semistable distribution is obtained. In the second part, considering the random field sampled at double random times, a mixture distribution is established for the limiting distribution of the maximum.

Relationship between Extremal and Sum Processes Generated by the same Point Process

Pancheva, E., Mitov, I., Volkovich, Z. (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.We discuss weak limit theorems for a uniformly negligible triangular array (u.n.t.a.) in Z = [0, ∞) × [0, ∞)^d as well as for the associated with it sum and extremal processes on an open subset S . The complement of S turns out to be the explosion area of the limit Poisson point process. In order to prove our criterion for weak convergence of the sum processes we introduce and study sum processes over explosion area....

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