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Title: Relationship between Extremal and Sum Processes Generated by the same Point Process
Authors: Pancheva, E.
Mitov, I.
Volkovich, Z.
Keywords: Extremal Processes
Increasing Processes with Independent Increments
Weak Limit Theorems
Levy Measure
Poisson Point Processes
Bernoulli Point Processes
Random Sample Size
Issue Date: 2009
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 35, No 2, (2009), 169p-194p
Abstract: 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. Finally we generalize the model of u.n.t.a. to random sample size processes.
Description: 2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.
ISSN: 1310-6600
Appears in Collections:Volume 35, Number 2

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