Nearest neighbour distance and dimension of intensity measure of Poisson point process

DOI10.1090/S0002-9939-2010-10467-7zbMath1226.60073OpenAlexW2046110621MaRDI QIDQ3082285

Radosław Wieczorek

Publication date: 10 March 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2010-10467-7

zbMATH Keywords

Poisson point processesprobability measurenearest neighbour distanceupper and lower local dimension

Mathematics Subject Classification ID

Fractals (28A80) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Cites Work

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• The infinite number of generalized dimensions of fractals and strange attractors
• Statistical description of chaotic attractors: the dimension function
• Estimation of dimension for spatially distributed data and related limit theorems
• On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions
• Coincidence of various dimensions associated with metrics and measures on metric spaces
• Pointwise dimensions and Rényi dimensions
• An Introduction to the Theory of Point Processes
• Statistical Analysis and Modelling of Spatial Point Patterns
• Measure and integration theory. Transl. from the German by Robert B. Burckel

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