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A two-dimensional ‘immigration–branching' model with application to earthquake occurrence times and energies

Published online by Cambridge University Press:  14 July 2016

C. D. Lai
C. D. Lai*
Affiliation:
University of Auckland
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Abstract

A two-dimensional Poisson cluster point process is formulated by the use of a probability generating functional. Moment measures of both the cluster centre and member processes are discussed. An example is provided, and the magnitude frequency law is proved in this case.

Keywords

PROBABILITY GENERATING FUNCTIONALPOISSON CLUSTERENERGIESEARTHQUAKE OCCURRENCESMAGNITUDE–FREQUENCY LAWMOMENT MEASURES
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 464 - 474
Copyright
Copyright © Applied Probability Trust 1977 

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References

Bartlett, M. S. and Kendall, D. G. (1951) On the use of the characteristic functional in the analysis of some stochastic processes occurring in physics and biology. Prob. Camb. Phil. Soc. 47, 65–67.Google Scholar
Feller, W. (1968) An Introduction to Probability Theory and its Applications , Vol. 1, 3rd edn. Wiley, New York.Google Scholar
Hawkes, A. G. (1971a) Spectra of some self-exciting and mutually exciting point processes. Biometrika 58, 83–90.CrossRefGoogle Scholar
Hawkes, A.G. (1971b) Point spectra of some mutually exciting point processes. J. R. Statist. Soc. B 33, 438–443.Google Scholar
Hawkes, A. G. and Oakes, D. (1974) A cluster process representation of a self-exciting process. J. Appl. Prob. 11, 493–503.Google Scholar
Kagan, Ya. Ya. (1973) A probabilistic description of the seismic regime (in Russian). Fizika Zemli 4, 10–23. English translation in Phys. Solid Earth 4, 213–219.Google Scholar
Kendall, D. G. (1949) Stochastic processes and population growth. J. R. Statist. Soc. B 11, 230–264.Google Scholar
Vere-Jones, D. (1968) Some applications of probability generating functionals to the study of input-output streams. J. R. Statist. Soc. B 30, 321–333.Google Scholar
Vere-Jones, D. (1970) Stochastic models for earthquake occurrences. J. R. Statist. Soc. B 32, 1–62.Google Scholar
Westcott, M. (1971) On existence and mixing results for cluster point processes. J. R. Statist. Soc. B 33, 290–300.Google Scholar
Westcott, M. (1972) The probability generating functional. J. Austral. Math. Soc. 14, 448–466.Google Scholar