On Lewis’ Simulation Method for Point Processes

IEEE Transactions on Information Theory

Volumn 27, Issue 1, 1981, Pages 23-31

  Ogaata, Yosihiko ^a  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL STATISTICS;

EID: 0019396823     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1981.1056305     Document Type: Article

References (14)

1. H. Akaike, “On entropy maximization principle,” Application of Statistics, P. R. Krishnaiah, Ed. Amsterdam: North-Holland, 1976, pp. 27–41.
2. H. Akaike, G. Kitagawa, E. Arahata, and F. Tada, “TIMSAC-78,” Computer Science Monographs, Institute of Statistical Mathematics, Tokyo, 1979.
3. K. B. Athreya, R. L. Tweedie, and D. Vere-Jones “Asymptotic behavior of point processes with Markov-dependent intervals,” Math. Nachrichten, 1981, to be published.
4. A. G. Hawkes, “Spectra of some self-exciting and mutually exciting point processes,” Biometrika, Vol. 58, pp. 83–95, 1971.
5. A. G. Hawkes, and D. A. Oakes, “A cluster process representation of a self-exciting process,” J. Appl. Prob., Vol. 11, pp. 493–503, 1974.
6. V. Isham, and M. Westcott, “A self-correcting point process,” Stoc. Proc. Appl., Vol. 8, pp. 335–348, 1979.
7. J. Jacod, “Multivariate point processes: Predictable projection, Radon-Nikodym derivatives, representation of martingales,” Z. f. Wahr. verw. Geb., Vol. 31, pp. 235–253, 1975.
8. Yu. M. Kabanov, R. S. Lipcer, and A. N. Shiryaev, “Criteria of absolute continuity of measures corresponding to multivariate point processes,” in Proc. 3rd U.S.S.R. and Japan Symposium on Probability Theory. Berlin: Springer, pp. 232–252, 1976.
9. P. A. W. Lewis, and G. S. Shedler, “Simulation of nonhomogeneous homogeneous Poisson processes by thinning,” Naval Res. Logistics Quart., Vol. 26, No. 3, pp. 403–413, 1979.
10. Y. Ogata, “The asymptotic behavior of maximum likelihood estimators for stationary point processes,” Ann. Inst. Stat. Math., Vol. 30, No. 2, A, pp. 243–261, 1978.
11. T. Ozaki, “Maximum likelihood estimation of Hawkes’ self-exciting point processes,” Ann. Inst. Stat. Math., Vol. 30, No. 3, B, pp. 145–155, 1978.
12. T. Ozaki, and H. Akaike, “On a generalized parametric model for Hawkes self-exciting point processes,” Institute of Statistical Mathematics, Tokyo, Japan, Res. Memo., No. 149, 1979.
13. Y. Sakamoto and H. Akaike, “Analysis of cross classified data by AIC,” Ann. Inst. Stat. Math., Vol. 30, No. 1, B, pp. 185–197, 1978.
14. D. Vere-Jones, “Earthquake prediction—A statistician's view,” J. Phys. Earth, Vol. 26, pp. 129–146, 1978.