Self-crossing Points of a Line Segment Process
Zbyněk Pawlas ()
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Zbyněk Pawlas: Charles University in Prague
Methodology and Computing in Applied Probability, 2014, vol. 16, issue 2, 295-309
Abstract This paper is devoted to planar stationary line segment processes. The segments are assumed to be independent, identically distributed, and independent of the locations (reference points). We consider a point process formed by self-crossing points between the line segments. Its asymptotic variance is explicitly expressed for Poisson segment processes. The main result of the paper is the central limit theorem for the number of intersection points in expanding rectangular sampling window. It holds not only for Poisson processes of reference points but also for stationary point processes satisfying certain conditions on absolute regularity (β-mixing) coefficients. The proof is based on the central limit theorem for β-mixing random fields. Approximate confidence intervals for the intensity of intersections can be constructed.
Keywords: Absolute regularity coefficient; Asymptotic variance; Central limit theorem; Independent marking; Intensity of intersections; Poisson process; Segment process; 60D05; 60F05; 60G55; 62G20 (search for similar items in EconPapers)
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