Self-excited (Hawkes) branching processes

Kiyoshi Kanazawa and Didier Sornette, Ubiquitous power law scaling in nonlinear self-excited Hawkes processes, Phys. Rev. Letts. 127 (18), 188301, pp. 1-6 (2021) (external pagehttp://arxiv.org/abs/2102.00242)

Alexander Wehrli, Spencer Wheatley and Didier Sornette,
Scale-, time- and asset-dependence of Hawkes process parameters estimated on high frequency price change data, Quantitative Finance 21 (5), 729-752, (2021)
(external pagehttps://doi.org/10.1080/14697688.2020.1838602)
(external pagehttp://ssrn.com/abstract=3597938)

Kiyoshi Kanazawa and Didier Sornette
Non-universal power law distribution of intensities of the self-excited Hawkes process: a field-theoretical approach,
Phys. Rev. Letts 125, 138301 (1-6) (2020)
(external pagehttp://arxiv.org/abs/2001.01195)

Kiyoshi Kanazawa and Didier Sornette
Field master equation theory of the self-excited Hawkes process,
Phys. Rev. Research 2, 033442 (1-28) (2020)
(external pagehttp://arxiv.org/abs/2001.01197)

Spencer Wheatley, Alexander Wehrli and Didier Sornette, The endo-exo problem in high frequency financial price fluctuations and rejecting criticality, Quantitative Finance 19 (7), 1165-1178 (2019)
Swiss Finance Institute Research Paper No. 18-57. Available at SSRN: external pagehttps://ssrn.com/abstract=3239443

A. Saichev and D. Sornette, Statistics of seismic cluster durations, Phys. Rev. E (submitted August 23, 2017)
(external pagehttp://arxiv.org/abs/1708.06970)

Spencer Wheatley, Vladimir Filimonov and Didier Sornette, Estimation of the Hawkes Process with Renewal Immigration using the EM Algorithm, Computational Statistics and Data Analysis 94, 120-135 (2016)
(external pagehttp://arxiv.org/abs/1407.7118 and external pagehttp://ssrn.com/abstract=2477432)

V. Filimonov, S. Wheatley, and D. Sornette, Effective measure of endogeneity for the Autoregressive Conditional Duration point processes via mapping to the self-excited Hawkes process, Communications in Nonlinear Science and Numerical Simulation 22(1-3), 23–37 (2015) external page(http://arxiv.org/abs/1306.2245)

D. Sornette, T. Maillart and G. Ghezzi, How Much is the Whole Really More than the Sum of its Parts? $1 \boxplus 1 = 2.5$: Superlinear Productivity in Collective Group Actions, PLoS ONE 9(8): e103023. doi:10.1371/journal.pone.0103023 (15 pp) external page(http://arxiv.org/abs/1405.4298)

Vladimir Filimonov, David Bicchetti, Nicolas Maystre and Didier Sornette, Quantification of the High Level of Endogeneity and of Structural Regime Shifts in Commodity Prices, The Journal of International Money and Finance 42, 174-192 (2014)
external page(http://ssrn.com/abstract=2237392)

A. Saichev and D. Sornette, Super-linear scaling of offsprings at criticality in branching processes, Physical Review E 89, 012104 (2014)
external page(http://arxiv.org/abs/1305.0684)

A. Saichev and D. Sornette, Generation-by-Generation Dissection of the Response Function in Long Memory Epidemic Processes, European Physical Journal B 75, 343-355 (2010) doi: 10.1140/epjb/e2010-00121-7
external page(http://arXiv.org/abs/0904.0872)

A. Saichev and D. Sornette, Fertility Heterogeneity as a Mechanism for Power Law Distributions and Recurrence Times, Physical Review. E 87, 022815 (2013)
external page(http://arxiv.org/abs/1211.6062)

V. Filimonov and D. Sornette, Quantifying reflexivity in financial markets: towards a prediction of flash crashes, Phys. Rev. E 85 (5): 056108 (2012)
external page(http://arxiv.org/abs/1201.3572 and external pagehttp://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
external page(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) 
external page(http://arxiv.org/abs/1101.5564)

A. Saichev, T. Maillart and D. Sornette, Hierarchy of Temporal Responses of Multivariate Self-Excited Epidemic Processes, Eur. Phys. J.B. 86 (124), 1-19 (DOI: 10.1140/epjb/e2013-30493-9) (2013)
external page(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) 
external page(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)
external page(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)
external page(http://arxiv.org/abs/physics/0606001)

A. Saichev and D. Sornette, "Universal'' Distribution of Inter-Earthquake Times Explained, Phys. Rev. Letts. 97, 078501 (2006)
external page(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)
external page(http://arxiv.org/abs/physics/0412043)

A. Saichev and D. Sornette, Vere-Jones' Self-Similar Branching Model, Phys. Rev. E 72, 056122 (2005)
external page(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)
external page(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)
external page(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)
external page(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)
external page(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)
external page(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)
external page(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)
external page(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)
external page(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)
external page(http://arXiv.org/abs/cond-mat/0109318)

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