E. Bacry, S. Delattre, M. Hoffmann, and J. F. Muzy, Some limit theorems for Hawkes processes and application to financial statistics, Stochastic Process. Appl, vol.123, p.3054533, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00845004

E. Bacry, S. Delattre, M. Hoffmann, and J. F. Muzy, Modelling microstructure noise with mutually exciting point processes, Quant. Finance, vol.13, pp.65-77, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01313995

E. Bacry and J. F. Muzy, First-and second-order statistics characterization of Hawkes processes and non-parametric estimation, IEEE Trans. Inform. Theory, vol.62, p.3480107, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01313834

J. Barral, Y. Hu, and T. Madaule, The minimum of a branching random walk outside the boundary case, Bernoulli, vol.24, pp.801-841, 2018.

H. C. Berbee, Random walks with stationary increments and renewal theory, Mathematical Centre Tracts, vol.112, 1979.

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

J. Chevallier, Mean-field limit of generalized Hawkes processes, Stochastic Process. Appl, vol.127, p.3718099, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01217407

J. Chevallier, M. J. Cáceres, M. Doumic, and P. Reynaud-bouret, Microscopic approach of a time elapsed neural model, Math. Models Methods Appl. Sci, vol.25, p.3411353, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01159215

M. Costa, C. Graham, L. Marsalle, and V. C. Tran, Renewal in Hawkes Processes with Self-Excitation and Inhibition. Preprint, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01683954

D. J. Daley and D. Vere-jones, An introduction to the theory of point processes, Elementary theory and methods, vol.I, p.1950431, 2003.

D. J. Daley and D. Vere-jones, An introduction to the theory of point processes, General theory and structure, vol.II, p.2371524, 2008.

S. Delattre and N. Fournier, Statistical inference versus mean field limit for Hawkes processes, Electron. J. Stat, vol.10, pp.1223-1295, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01367752

S. Delattre, N. Fournier, and M. Hoffmann, Hawkes processes on large networks, Ann. Appl. Probab, vol.26, pp.216-261, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01102806

S. Ditlevsen and E. Löcherbach, Multi-class oscillating systems of interacting neurons, Stochastic Process. Appl, vol.127, p.3646433, 2017.

A. Duarte, E. Löcherbach, and G. Ost, Stability, convergence to equilibrium and simulation of non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels, 2016.

F. Guillemin and A. Simonian, Transient characteristics of an M/M/? system, vol.27, p.1341889, 1995.
URL : https://hal.archives-ouvertes.fr/inria-00074289

A. G. Hawkes, Spectra of some self-exciting and mutually exciting point processes, Biometrika, vol.58, p.278410, 1971.

A. G. Hawkes and L. Adamopoulos, Cluster Models for Earthquakes: Regional Comparisons, Bull. Int. Statist. Inst, vol.45, pp.454-461, 1973.

A. G. Hawkes and D. Oakes, A cluster process representation of a selfexciting process, J. Appl. Probability, vol.11, pp.493-503, 1974.

Y. Hu, How big is the minimum of a branching random walk?, Ann. Inst. Henri Poincaré Probab. Stat, vol.52, pp.233-260, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00826652

T. Jaisson and M. Rosenbaum, Limit theorems for nearly unstable Hawkes processes, Ann. Appl. Probab, vol.25, p.3313750, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01138784

T. Jaisson and M. Rosenbaum, Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes, Ann. Appl. Probab, vol.26, pp.2860-2882, 2016.

N. N. Lebedev, Special functions and their applications, 1965.

B. Mallein, Genealogy of the extremal process of the branching random walk, ALEA Lat. Am. J. Probab. Math. Stat, vol.15, p.3852245, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01326628

P. Massart, Concentration inequalities and model selection, Berlin Lectures from the 33rd Summer School on Probability Theory, 2003.

J. Möller and J. G. Rasmussen, Perfect simulation of Hawkes processes, Adv. in Appl. Probab, vol.37, p.2156552, 2005.

Y. Ogata, Statistical models for earthquake occurrences and residual analysis for point processes, Journal of American Statistical Association, vol.83, pp.9-27, 1988.

P. Reynaud-bouret, V. Rivoirard, and C. Tuleau-malot, Inference of functional connectivity in Neurosciences via Hawkes processes, 1st IEEE Global Conference on Signal and Information Processing, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00866823

P. Reynaud-bouret and E. Roy, Some non asymptotic tail estimates for Hawkes processes, Bull. Belg. Math. Soc. Simon Stevin, vol.13, p.2293215, 2006.

P. Reynaud-bouret and S. Schbath, Adaptive estimation for Hawkes processes; application to genome analysis, Ann. Statist, vol.38, pp.2781-2822, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00863958

P. Robert, Stochastic networks and queues, French ed. Applications of Mathematics, vol.52, p.1996883, 2003.

W. Rudin, Real and complex analysis, p.2, 1987.

Z. Shi, Branching random walks, Cham 42nd Saint Flour Probability Summer School, p.3444654, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01275563

L. Takács, On a probability problem arising in the theory of counters, Proc. Cambridge Philos. Soc, vol.52, p.81585, 1956.

L. Takács, Introduction to the theory of queues. University Texts in the Mathematical Sciences, 1962.

H. Thorisson, Coupling, stationarity, and regeneration. Probability and its Applications, 2000.

D. V. Widder, The Laplace Transform, Princeton Mathematical Series, issue.6, 1941.