Self-excited (Hawkes) branching processes

V. Filimonov and D. Sornette, Quantifying reflexivity in financial markets: towards a prediction of flash crashes, Phys. Rev. E 85 (5): 056108 (2012)
(http://arxiv.org/abs/1201.3572 and http://ssrn.com/abstract=1998832)

V.A. Filimonov and D. Sornette, Self-Excited Multifractal Dynamics, Europhysics Letters 94, 46003 (2011) doi: 10.1209/0295-5075/94/46003
(http://arxiv.org/abs/1008.1430)

A. Saichev and D. Sornette, Generating Functions and Stability Study of Multivariate Self-Excited Epidemic Processes, European Physical Journal B 83, 271-282 (2011)
(http://arxiv.org/abs/1101.5564)

A. Saichev and D. Sornette, Hierarchy of Temporal Responses of Multivariate Self-Excited Epidemic Processes, Physical Review E (submitted 8 January, 2011)
(http://arxiv.org/abs/1101.1611)

D. Sornette and S. Utkin, Limits of Declustering Methods for Disentangling Exogenous from Endogenous Events in Time Series with Foreshocks, Main shocks and Aftershocks, Physical Review E 79, 061110 (2009)
(http://arxiv.org/abs/0903.3217)

D. Sornette, S. Utkin and A. Saichev, Solution of the Nonlinear Theory and Tests of Earthquake Recurrence Times, Physical Review E 77, 066109 (2008)
(http://arxiv.org/abs/0712.2335)

A. Saichev and D. Sornette, Theory of Earthquake Recurrence Times, J. Geophys. Res., 112, B04313, doi:10.1029/2006JB004536 (2007)
(http://arxiv.org/abs/physics/0606001)

A. Saichev and D. Sornette, "Universal'' Distribution of Inter-Earthquake Times Explained, Phys. Rev. Letts. 97, 078501 (2006)
(http://arxiv.org/abs/physics/0604018)

A. Saichev and D. Sornette, Power law distribution of seismic rates: theory and data, Eur. Phys. J. B 49, 377-401 (2006)
(http://arxiv.org/abs/physics/0412043)

A. Saichev and D. Sornette, Vere-Jones' Self-Similar Branching Model, Phys. Rev. E 72, 056122 (2005)
(http://arxiv.org/abs/cond-mat/0505644)

A. Saichev, A. Helmstetter and D. Sornette, Anomalous Scaling of Offspring and Generation Numbers in Branching Processes, Pure and Applied Geophysics 162, 1113-1134 (2005)
(http://arXiv.org/abs/cond-mat/0305007)

A. Saichev and D. Sornette, Anomalous Power Law Distribution of Total Lifetimes of Aftershock Sequences, Phys. Rev. E 70, 046123 (2004)
(http://arXiv.org/abs/physics/0404019)

A. Helmstetter and D. Sornette, Foreshocks explained by cascades of triggered seismicity, J. Geophys. Res., 108 (B10), 2457, 10.1029/2003JB002409 01 (2003)
(http://arXiv.org/abs/physics/0210130)

A. Helmstetter and D. Sornette, Predictability in the ETAS Model of Interacting Triggered Seismicity, J. Geophys. Res., 108,  2482,  10.1029/2003JB002485 (2003)
(http://arXiv.org/abs/cond-mat/0208597)

A. Helmstetter and D. Sornette, Importance of direct and indirect triggered seismicity
in the ETAS model of seismicity, Geophys. Res. Lett. 30 (11), 10.1029/2003GL017670 (2003)
(http://arXiv.org/abs/physics/0303070)

A. Helmstetter, D. Sornette and J.-R. Grasso, Mainshocks are Aftershocks of Conditional Foreshocks: How do foreshock statistical properties emerge from aftershock laws, J. Geophys. Res., 108 (B10), 2046, 10.1029/2002JB001991 (2003)
(http://arXiv.org/abs/cond-mat/0205499)

A. Helmstetter and D. Sornette, Diffusion of epicenters of earthquake aftershocks, Omori's law, and generalized continuous-time random walk models - art. no. 061104, Physical Review E. 6606 (6 Part 1):1104, 10.1103/PhysRevE.66.061104 (2002)
(http://arXiv.org/abs/cond-mat/0203505)

D. Sornette and A. Helmstetter, Occurrence of Finite-Time-Singularity in Epidemic Models of Rupture, Earthquakes and Starquakes, Physical Review Letters 89 (15) 158501 (2002)
(http://arXiv.org/abs/cond-mat/0112043)

A. Helmstetter and D. Sornette, Sub-critical and supercritical regimes in epidemic models of earthquake aftershocks, J. Geophys. Res. 107, NO. B10, 2237, 10.1029/2001JB001580 (2002)
(http://arXiv.org/abs/cond-mat/0109318)