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Corners and records of the Poisson process in quadrant. (English) Zbl 1191.60064

Summary: The scale-invariant spacings lemma due to R. Arratia, A. D. Barbour and S. Tavaré [Comb. Probab. Comput. 15, No. 1–2, 31–62 (2006; Zbl 1086.60005)] establishes the distributional identity of a self-similar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the unit Poisson process in the positive quadrant

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G70 Extreme value theory; extremal stochastic processes

Citations:

Zbl 1086.60005
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