S. Arlot and P. Massart, Data-driven calibration of penalties for leastsquares regression, J. Mach. Learn. Res, vol.10, pp.245-279, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00287631

Y. Baraud, F. Comte, and G. Viennet, Model selection for (auto-)regression with dependent data, ESAIM: Probability and Statistics, vol.5, pp.33-49, 2001.
DOI : 10.1051/ps:2001101

URL : https://hal.archives-ouvertes.fr/hal-00170758

Y. Baraud, F. Comte, and G. Viennet, Adaptive estimation in autoregression or beta-mixing regression via model selection, Ann. Statist, vol.39, pp.839-875, 2001.

L. Birgé, A New Lower Bound for Multiple Hypothesis Testing, IEEE Transactions on Information Theory, vol.51, issue.4, pp.1611-1615, 2005.
DOI : 10.1109/TIT.2005.844101

L. Birgé and P. Massart, Gaussian model selection, Journal of the European Mathematical Society, vol.3, issue.3, pp.203-268, 2001.
DOI : 10.1007/s100970100031

L. Birgé and P. Massart, Minimal Penalties for Gaussian Model Selection, Probability Theory and Related Fields, vol.6, issue.1-2, pp.33-73, 2007.
DOI : 10.1007/s00440-006-0011-8

P. Brémaud and L. Massoulié, Stability of nonlinear Hawkes processes, Ann. Probab, vol.24, pp.1563-1588, 1996.

P. Brémaud and L. Massoulié, Hawkes branching point processes without ancestors, Journal of Applied Probability, vol.38, issue.01, pp.122-135, 2001.
DOI : 10.1093/biomet/58.1.83

D. J. Daley, V. , and D. , An Introduction to the Theory of Point Processes. Springer Series in Statistics I.S p r i n g e r ,N e wY o r k, p.950166, 2005.

R. Gallager, Information Theory and Reliable Communication, 1968.
DOI : 10.1007/978-3-7091-2945-6

G. Gusto, Estimation de l'intensité d'un processus de Hawkes généralisé double ApplicationàApplication`Applicationà la recherche de motifsc o r ´ e p a r t i sl e long d'une séquence d'ADN, 2004.

G. Gusto and S. Schbath, FADO: A Statistical Method to Detect Favored or Avoided Distances between Occurrences of Motifs using the Hawkes' Model, Statistical Applications in Genetics and Molecular Biology, vol.4, issue.1, 2005.
DOI : 10.2202/1544-6115.1119

A. G. Hawkes and D. Oakes, A cluster process representation of a self-exciting process, Journal of Applied Probability, vol.33, issue.03, pp.493-503, 1974.
DOI : 10.2307/3212006

C. Lacour, Adaptive estimation of the transition density of a Markov chain, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.43, issue.5, pp.571-597, 2007.
DOI : 10.1016/j.anihpb.2006.09.003

URL : https://hal.archives-ouvertes.fr/hal-00115617

P. Massart, Concentration Inequalities and Model Selection. Lecture Notes in Math. 1896.S p r i n g e r ,B e r l i n, p.2319879, 2007.

Y. Ogata and H. Akaike, On Linear Intensity Models for Mixed Doubly Stochastic Poisson and Self-exciting Point Processes, J. Roy. Statist. Soc. Ser. B, vol.44, pp.102-107, 1982.
DOI : 10.1007/978-1-4612-1694-0_20

T. Ozaki, Maximum likelihood estimation of Hawkes' self-exciting point processes, Annals of the Institute of Statistical Mathematics, vol.18, issue.1, pp.145-155, 1979.
DOI : 10.1007/BF02480272

G. Reinert, S. Schbath, and M. S. Wat-e-r-m-a-n, Probabilistic and Statistical Properties of Words: An Overview, Journal of Computational Biology, vol.7, issue.1-2, pp.1-46, 2000.
DOI : 10.1089/10665270050081360

P. Reynaud-bouret, Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities, Probability Theory and Related Fields, vol.126, issue.1, pp.103-153, 2003.
DOI : 10.1007/s00440-003-0259-1

P. Reynaud-bouret, Compensator and exponential inequalities for some suprema of counting processes, Statistics & Probability Letters, vol.76, issue.14, pp.1514-1521, 2006.
DOI : 10.1016/j.spl.2006.03.012

P. Reynaud-bouret, Penalized projection estimators of the Aalen multiplicative intensity, Bernoulli, vol.12, issue.4, pp.633-661, 2006.
DOI : 10.3150/bj/1155735930

P. Reynaud-bouret and E. Roy, Some nonasymptotic tail estimate for Hawkes processes, Bull. Belg. Math. Soc. Simon Stevin, vol.13, pp.883-896, 2007.

P. Reynaud-bouret and S. Schbath, Adaptive estimation for Hawkes'processes; application to genome analysis Available at, 2010.

D. Vere-jones and T. Ozaki, Some examples of statistical estimation applied to earthquake data, Annals of the Institute of Statistical Mathematics, vol.26, issue.3, pp.189-207, 1982.
DOI : 10.1007/BF02481022

E. France, reynaudb@unice.fr Institut National de la Recherche Agronomique UnitéM a t h ´ ematique, Informatique et Génome Domaine de Vilvert F-78352 Jouy-en-Josas Cedex France E-mail: Sophie