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The Markovian self-exciting process

Published online by Cambridge University Press:  14 July 2016

David Oakes
David Oakes*
Affiliation:
Harvard University
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Abstract

The self-exciting point process with exponential exciting function is investigated using the immigration birth representation of the process. The counting distribution is derived explicitly and some simpler interval properties are given. In particular, it is shown that the serial covariances of the interval sequence decrease monotonically to zero.

Keywords

POINT PROCESSSELF-EXCITING POINT PROCESSMARKOVIAN SELF-EXCITING POINT PROCESSIMMIGRATION-BIRTH PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 69 - 77
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
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[3] Hawkes, A. G. (1971) Spectra of some self-exciting and mutually exciting point processes. Biometrika 58, 83–90.Google Scholar
[4] Hawkes, A. G. and Oakes, D. (1974) A cluster process representation of a self-exciting process. J. Appl. Prob. 11, 493–503.Google Scholar
[5] Yang, Y. S. (1972) On branching processes allowing immigration. J. Appl. Prob. 9, 24–31.CrossRefGoogle Scholar