REFERENCES
- Borovkov , A.A. Boundary values problems for random walks and large deviations for function spaces . Theory Probab. Appl. 1967 , 12 , 575 – 595 .
- Brémaud , P. ; Massoulié , L. Stability of nonlinear Hawkes processes . Ann. Prob. 1996 , 24 , 1563 – 1588 .
- Brémaud , P. ; Massoulié , L. ; Ridolfi , A. Power spectra of random spike fields and related processes . Adv. Appl. Prob. 2005 , 37 , 1116 – 1146 .
- Brémaud , P. ; Nappo , G. ; Torrisi , G.L. Rate of convergence to equilibrium of marked Hawkes processes . J. Appl. Prob. 2002 , 39 , 123 – 136 .
- Brix , A. ; Chadoeuf , J. Spatio-temporal modeling of weeds by shot-noise G Cox processes . Biometrical J. 2002 , 44 , 83 – 99 .
- Chavez-Demoulin , V. ; Davison , A.C. ; Mc Neil , A.J. Estimating value-at-risk: a point process approach . Quantitative Finance. 2005 , 5 , 227 – 234 .
- Daley , D.J. ; Vere-Jones , D. An Introduction to the Theory of Point Processes, , 2nd Ed.; Springer : New York , 2003.
- de Acosta , A. Large deviations for vector valued Lévy processes . Stochastic Process. Appl. 1994 , 51 , 75 – 115 .
- Dembo , A. ; Zeitouni , O. Large Deviations Techniques and Applications, , 2nd Ed. ; Springer : New York , 1998 .
- Ganesh , A. ; Macci , C. ; Torrisi , G.L. Sample path large deviations principles for Poisson shot noise processes and applications . Electron. J. Probab. 2005 , 10 , 1026 – 1043 .
- Gusto , G. ; Schbath , S. F.A.D.O.: A statistical method to detect favored or avoided distances between occurrences of motifs using the Hawkes model . Stat. Appl. Genet. Mol. Biol. 2005 , 4 , Article 24 .
- Hawkes , A.G. Spectra of some self-exciting and mutually exciting point processes . Biometrika 1971 , 58 , 83 – 90 .
- Hawkes , A.G. Point spectra of some mutually exciting point processes . J. Roy. Statist. Soc. Ser. B 1971 , 33 , 438 – 443 .
- Hawkes , A.G. ; Oakes , D. A cluster representation of a self-exciting process . J. Appl. Prob. 1974 , 11 , 493 – 503 .
- Jagers , P. Branching Processes with Biological Applications ; John Wiley : London , 1975 .
- Jonnson , D.H. Point process models of single-neuron discharges . J. Computational Neuroscience 1996 , 3 , 275 – 299 .
- Kerstan , J. Teilprozesse poissonscher prozesse. Transactions of the Third Prague Conference on Information Theory, Statistical Decision Functions, Random Processes 1964 ; 377 – 403 .
- Massoulié , L. Stability results for a general class of interacting point processes dynamics, and applications . Stoch. Proc. Appl. 1998 , 75 , 1 – 30 .
- M⊘ller , J. A comparison of spatial point process models in epidemiological applications . In Highly Structured Stochastic Systems ; Green , P.J. ; Hjort , N.L. ; Richardson , S. , Eds; Oxford University Press , 2003 ; 264 – 268 .
- M⊘ller , J. Shot noise Cox processes . Adv. Appl. Prob. 2003 , 35 , 614 – 640 .
- M⊘ller , J. ; Rasmussen , J.G. Perfect simulation of Hawkes processes . Adv. Appl. Prob. 2005 , 37 , 629 – 646 .
- M⊘ller , J. ; Torrisi , G.L. Generalised shot noise Cox processes . Adv. Appl. Prob. 2005 , 37 , 48 – 74 .
- M⊘ller , J. ; Torrisi , G.L. The pair correlation function of spatial Hawkes processes . Stat. Probab. Lett. 2007 , 77 , 995 – 1003 .
- M⊘ller , J. ; Waagepetersen , R.S. Statistical Inference and Simulation for Spatial Point Processes ; Chapman and Hall : Boca Raton , 2004 .
- Neyman , J. ; Scott , E.L. Statistical approach to problems of cosmology . J. R. Statist. Soc. B 1958 , 20 , 1 – 43 .
- Ogata , Y. Statistical models for earthquake occurrences and residual analysis for point processes . J. Amer. Statist. Assoc. 1988 , 83 , 9 – 27 .
- Ogata , Y. Space-time point process model for earthquake occurrences . Ann. Inst. Statist. Math. 1998 , 50 , 379 – 402 .
- Ogata , Y. ; Akaike , H. On linear intensity models for mixed doubly stochastic poisson and self-exciting point processes . J. R. Statist. Soc. B 1982 , 44 , 102 – 107 .
- Reynaud-Bouret , P. ; Roy , E. Some non asymptotic tail estimates for Hawkes processes . Bull. Belg. Math. Soc. Simon Stevin 2007 , 13 , 883 – 896 .
- Stabile , G. ; Torrisi , G.L. Risk processes with non-stationary Hawkes arrivals . Submitted . 2007 .
- Torrisi , G.L. A class of interacting marked point processes: rate of convergence to equilibrium . J. Appl. Prob. 2002 , 39 , 137 – 161 .
- Vere-Jones , D. ; Ozaki , T. Some examples of statistical estimation applied to earthquake data . Ann. Inst. Statist. Math. 1982 , 34 , 189 – 207 .