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Laws of large numbers in self-correcting point processes

Author

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  • Hayashi, T.

Abstract

For a point process N(·) with the conditional intensity function [psi](t> - N(t)), the process t - N(t) has the Markov property, where [psi](·) is a function satisfying suitable conditions. It follows from the properties of [psi](·) that the Markov process t - N(t) is ergodic (i.e. positive recurrent). This result leads to the law of large numbers for functionals of the Markov process t - N(t).

Suggested Citation

  • Hayashi, T., 1986. "Laws of large numbers in self-correcting point processes," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 319-326, December.
    • Handle: RePEc:eee:spapps:v:23:y:1986:i:2:p:319-326
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    Cited by:

    1. Takayuki Fujii & Yoichi Nishiyama, 2012. "Some problems in nonparametric inference for the stress release process related to the local time," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 991-1007, October.
    2. Nobuo Inagaki & Toshihabu Hayashi, 1990. "Parameter estimation for the simple self-correcting point process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 89-98, March.

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