Approximate simulation of Hawkes processes

Methodology and Computing in Applied Probability

Volumn 8, Issue 1, 2006, Pages 53-64

  Møller, Jesper ^a   Rasmussen, Jakob G ^a  

^a AALBORG UNIVERSITY   (Denmark)

Author keywords

Edge effects; Hawkes process; Marked point process; Poisson cluster process; Simulation

Indexed keywords

EID: 33747601330     PISSN: 13875841     EISSN: 15737713     Source Type: Journal    
DOI: 10.1007/s11009-006-7288-z     Document Type: Article

References (18)

1. T. M. Apostol, Mathematical Analysis, Addison-Wesley, Reading, 1974.
2. P. Brémaud and L. Massoulié, "Hawkes branching point processes without ancestors," Journal of Applied Probability vol. 38 pp. 122-135, 2001.
3. P. Brémaud and L. Massoulié, "Power spectra of general shot noises and Hawkes point processes with a random excitation," Advances in Applied Probability vol. 34 pp. 205-222, 2002.
4. P. Brémaud, G. Nappo, and G. L. Torrisi, "Rate of convergence to equilibrium of marked Hawkes processes," Journal of Applied Probability vol. 39 pp. 123-136, 2002.
5. E. S. Chornoboy, L. P. Schramm, and A. F. Karr, "Maximum likelihood identification of neural point process systems," Advances in Applied Probability vol. 34 pp. 267-280, 2002.
6. D. J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes, Volume I: Elementary Theory and Methods 2nd edition, Springer: New York, 2003.
7. A. G. Hawkes, "Spectra of some self-exciting and mutually exciting point processes," Biometrika vol. 58(1) pp. 83-90, 1971a.
8. A. G. Hawkes, "Point spectra of some mutually exciting point processes," J. Roy. Statist. Soc. Ser. B vol. 33 pp. 438-443, 1971b.
9. A. G. Hawkes, "Spectra of some mutually exciting point processes with associated variables." In P. A. W. Lewis (ed.), Stochastic Point Processes, pp. 261-271, Wiley: New York, 1972.
10. A. G. Hawkes and L. Adamopoulos, "Cluster models for earthquakes-regional comparisons," Bulletin of the International Statistical Institute vol. 45 pp. 454-461, 1973.
11. A. G. Hawkes and D. Oakes, "A cluster representation of a self-exciting process," Journal of Applied Probability vol. 11 pp. 493-503, 1974.
12. T. Lindvall, Lectures on the Coupling Method, Wiley: New York, 1992.
13. J. Moøller and J. G. Rasmussen, "Perfect simulation of Hawkes processes". Research report R-2004-18, Department of Mathematical Sciences, Aalborg University. Available at http://www.math.aau.dk/jm, 2004.
14. Y. Ogata, "On Lewis' simulation method for point processes," IEEE Transactions on Information Theory vol. IT-27(1) pp. 23-31, 1981.
15. Y. Ogata, "Statistical models for earthquake occurrences and residual analysis for point processes," Journal of the American Statistical Association vol. 83(401) pp. 9-27, 1988.
16. Y. Ogata, "Space-time point-process models for earthquake occurrences," Annals of the Institute of Statistical Mathematics vol. 50(2) pp. 379-402, 1998.
17. G. L. Torrisi, "A class of interacting marked point processes: Rate of convergence to equilibrium," Journal of Applied Probability vol. 39 pp. 137-160, 2002.
18. D. Vere-Jones and T. Ozaki, "Some examples of statistical inference applied to earthquake data," Annals of the Institute of Statistical Mathematics vol. 34 pp. 189-207, 1982.