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The second-order analysis of stationary point processes
Abstract
This paper provides a rigorous foundation for the second-order analysis of stationary point processes on general spaces. It illuminates the results of Bartlett on spatial point processes, and covers the point processes of stochastic geometry, including the line and hyperplane processes of Davidson and Krickeberg. The main tool is the decomposition of moment measures pioneered by Krickeberg and Vere-Jones. Finally some practical aspects of the analysis of point processes are discussed.
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Ripley's K-function with isotropic edge correction was computed following Ripley, and the centred Besag's L-function transformation was applied.
“For both protocols, Ripley’s Kfunction with isotropic edge correction was computed following Ripley66,67, and the centred Besag’s L-function transformation was applied68.”
From Ecological legacies of pre-columbian settlements evident in palm clusters of neotropical mountain forests (2026) · cites this paper as [66]
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Research works printed but not linked: 28
- 10.1017/S0305004100026153 · DOI
- Vere-Jones, 1968, Some applications of probability generating functionals to the study of input-output streams, J. R. Statist. Soc., 30, 321, 10.1111/j.2517-6161.1968.tb00732.x · DOI
- Silverman B. W. (1976) Limit theorems for dissociated random variables. J. Appl. Prob. Submitted for publication. · DOI
- Santaló, 1953, Introduction to Integral Geometry.
- Ripley B. D. (1976C) The foundations of stochastic geometry. Ann. Prob. Submitted for publication. · DOI
- Bartlett, 1967, The spectral analysis of line processes, Proc. 5th Berkeley Symp. Math. Statist. Prob., 3, 135
- 10.1016/S0006-3495(67)86597-4 · DOI
- Matern, 1960, Spatial variation, Meddelanden från Statens Skogsforskningsinstitut, 49, 5
- 10.1038/scientificamerican0475-34 · DOI
- Gel'fand, 1964, Generalized Functions, 4
- 10.1007/BF00535466 · DOI
- 10.1007/978-94-011-7801-3 · DOI
- Chriŝtensen, 1974, Topology and Borei Structure.
- 10.1093/biomet/51.3-4.299 · DOI
- Bourbaki, 1966, General Topology.
- 10.1111/j.1365-2818.1972.tb03713.x · DOI
- 10.1098/rspa.1950.0102 · DOI
- Vere-Jones, 1971, The covariance measure of a weakly stationary random measure, J. R. Statist. Soc., 33, 426
- Krickeberg K. (1973) Moments of point processes. In Harding and Kendall (1974), 89–113. · DOI
- 10.1007/BF02545761 · DOI
- Ripley B. D. (1976a) The disintegration of invariant measures. Math. Proc. Camb. Phil. Soc. , To appear. · DOI
- 10.1038/233067a0 · DOI
- 10.1017/S0001867800045407 · DOI
- 10.1093/biomet/62.2.467 · DOI
- Vere-Jones, 1970, Stochastic models for earthquake occurrence, J. R. Statist. Soc. B., 32, 1, 10.1111/j.2517-6161.1970.tb00814.x · DOI
- Nachbin, 1967, The Haar Integral.
- Bourbaki, 1963, Intégration, VII
- Davidson, 1970, Stochastic Geometry, 55
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Metadata
- Authors
- Ripley, B. D.
- Venue
- Journal of Applied Probability
- Publisher
- Cambridge University Press (CUP)
- Published
- 1976-06
- Volume
- 13
- Issue
- 2
- Pages
- 255-266
- ISSN
- 0021-9002
- 1475-6072
- Cited by
- 1,539
- References
- 0
- Language
- en
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