Stability of nonlinear Hawkes processes

Annals of Probability

Volumn 24, Issue 3, 1996, Pages 1563-1588

  Brémaud, Pierre ^a   Massoulié, Laurent ^a  

^a NONE

Author keywords

Hawkes processes; Mutually exciting point processes; Point processes; Stationary point processes; Stochastic intensity; Stochastic processes

Indexed keywords

EID: 0030352915     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1065725193     Document Type: Article

References (18)

1. ASMUSSEN, S. (1987). Applied Probability and Queues. Wiley, New York.
2. BACCELLI, F. and BRÉMAUD, P. (1994). Elements of Queueing Theory. Springer, New York.
3. BRÉMAUD, P. (1981). Point Processes and Queues. Springer, New York.
4. BRÉMAUD, P. and MASSOULIÉ, L. (1994). Imbedded construction of stationary point processes and sequences with a random memory. Queueing Systems 17 213-234.
5. DALEY, D. J. and VERE-JONES, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York.
6. HAWKES, A. G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika 58 83-90.
7. HAWKES, A. G. and OAKES, D. (1974). A cluster process representation of a self-exciting process. J. Appl. Probab. 11 493-503.
8. JACOD, J. (1975). Multivariate point processes: predictable projections, Radon-Nikodym derivatives, representation of martingales. Z. Wahrsch. Verw. Gebiete 31 235-253.
9. JACOD, J. (1979). Calcul stochastique et problèmes de martingales. Springer, Berlin.
10. KERSTAN, J. (1964). Teilprozesse Poissonscher Prozesse. Transactions of the Third Prague Conference on Information Theory, Statistical Decision Functions, Random Processes 377-403.
11. LAST, G. (1993). On dependent marking and thinning of point processes. Stochastic Process. Appl. 45 73-94.
12. LEWIS, P. A. W. and SHEDLER, G. S. (1976). Simulation of nonhomogeneous Poisson processes with log linear rate function. Biometrika 63 501-506.
13. LINDVALL, T. (1988). Ergodicity and inequalities in a class of point processes. Stochastic Process. Appl. 30 121-131.
14. LINDVALL, T. (1992). Lectures on the Coupling Method. Wiley, New York.
15. LIPTSER, R. S. and SHIRYAYEV, A. N. (1978). Statistics of Random Processes, II: Applications. Springer, New York.
16. MASSOULIÉ, L. (1995). Stabilité, simulation et optimisation de systèmes à événements discrets. Ph.D. thesis, Univ. Paris-sud.
17. NEVEU, J. (1965). Mathematical Foundations of the Calculus of Probability. Holden-Day, San Francisco.
18. OGATA, Y. (1981). On Lewis' simulation method for point processes. IEEE Trans. Inform. Theory 27 23-31.