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The asymptotic behaviour of maximum likelihood estimators for stationary point processes

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References

  1. Billingsley, P. (1961).Statistical Inference for Markov Process, The University of Chicago Press, Chicago

    MATH  Google Scholar 

  2. Billingsley, P. (1961). The Lindeberg-Lévy Theorem for martingales,Proc. Amer. Math. Soc.,12, 788–792.

    MathSciNet  MATH  Google Scholar 

  3. Dellacherie, C. (1972).Capacities et Processus Stochastiques, Springer-Verlag, Heidelberg.

    MATH  Google Scholar 

  4. Feller, W. (1966).An Introduction to Probability Theory and its Applications, Vol. 2. John Wiley & Sons, New York.

    MATH  Google Scholar 

  5. Hawkes, A. G. and Oakes, D. (1974). A cluster process representation of a self-exiting point process,J. Appl. Prob.,11, 493–503.

    Article  Google Scholar 

  6. Kavanov, Yu. M., Lipster, R. Sh. and Shiryaev, A. N. (1975). Martingale method in the theory of point processes (in Russian),Proceeding of Vilnius Symposium U.S.S.R.

  7. Meyer, P. A. (1972).Martingales and Stochastic Integrals I, Lecture Notes in Mathematics, 284, Springer, Berlin.

    MATH  Google Scholar 

  8. Ozaki, T. (1977). Maximum likelihood estimation of Hawkes' self-exciting point process,Research Memorandom, No. 115, The Institute of Statistical Mathematics, Tokyo.

    Google Scholar 

  9. Vere-Jones, D. (1973).Lectures on Point Processes, Department of Statistics, University of California, Berkeley.

    Google Scholar 

  10. Vere-Jones, D. (1975). On updating algorithms and inference for stochastic point processes,Perspectives in probability and statistics, Gani, J. ed., Applied Probability Trust.

  11. Aczel, J. (1966).Lectures on Functional Equations and their Applications, Academic Press, New York.

    MATH  Google Scholar 

  12. Daley, D. J. and Vere-Jones, D. (1972). A summary of the theory of point processes,Stochastic point processes: statistical analysis, theory and applications, Lewis, A. W. ed., Wiley, New York.

    MATH  Google Scholar 

  13. Huber, P. J. (1967). The behaviour of maximum likelihood estimates under nonstandard conditions,Proc. 5th Berkeley Symp. Math. Statist. Prob.,1, 221–233.

    Google Scholar 

  14. Meyer, P. A. (1966).Probability and Potentials, Blaisdell Publishing Co., Waltham.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Victoria University of Wellington, Wellington, Australia

    Yoshiko Ogata

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  1. Yoshiko Ogata
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The Institute of Statistical Mathematics

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Ogata, Y. The asymptotic behaviour of maximum likelihood estimators for stationary point processes. Ann Inst Stat Math 30, 243–261 (1978). https://doi.org/10.1007/BF02480216

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  • DOI: https://doi.org/10.1007/BF02480216

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