Fetching the paper…
Reading the bibliography…
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations.
E. Nyström, “”über die praktische auflsung von integralgleichungen mit anwendungen auf randwertaufgaben”,” Acta Mathematica , vol. 54, pp. 185–204, 1930
1930
Earlier work this paper cites.
N. Wiener and E. Hopf, “”üeber eine klasse singulärer integralgleichungen”,” Sem-Ber Preuss Akad Wiss , vol. 31, pp. 696–706, 1931
1931
Earlier work this paper cites.
I. Gokhberg and M. Krein, “Systems of integral equations on the half-line with kernels depending on the difference of the arguments,” Uspekhi Mat. Nauk , vol. 13, pp. 3–72, 1958
1958
Earlier work this paper cites.
B. Noble, Methods based on the Wiener-Hopf technique for the solution of partial differential equations . Pergamon, 1958
1958
Earlier work this paper cites.
E. Parzen, “”on estimation of a probability density function and mode”,” Annals of Mathematical Statistics , vol. 33, 1962
1962
Earlier work this paper cites.
M. S. Bartlett, “The spectral analysis of point processes,” Journal of the Royal Statistical Society. Series B (Methodological) , vol. 25, no. 2, pp. 264–296, Jan. 1963, ArticleType: research-article / Full publication date: 1963 / Copyright © 1963 Royal Statistical Society. [Online]. Available: http://www.jstor.org/stable/2984295
1963
Earlier work this paper cites.
——, “The spectral analysis of Two-Dimensional point processes,” Biometrika , vol. 51, no. 3/4, pp. 299–311, Dec. 1964, ArticleType: research-article / Full publication date: Dec., 1964 / Copyright © 1964 Biometrika Trust. [Online]. Available: http://www.jstor.org/stable/2334136
1964
Earlier work this paper cites.
A. Hawkes, “Spectra of some self-exciting and mutually exciting point processes,” Biometrika , vol. 58, pp. 83–90, April 1971
1971
Earlier work this paper cites.
——, “Point spectra of some mutually exciting point processes,” Journal of the Royal Statistical Society. Series B (Methodological) , vol. 33-3, pp. 438–443, April 1971
1971
Earlier work this paper cites.
K. Atkinson, A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind . Society for Industrial and Applied Mathematics, 1976
1976
Earlier work this paper cites.
T. Ozaki, “Maximum likelihood estimation of hawkes’ self-exciting point processes,” Annals of the Institute of Statistical Mathematics , vol. 31, no. 1, pp. 145–155, Dec. 1979. [Online]. Available: http://www.springerlink.com/content/hr3q7667x3522235/
1979
Earlier work this paper cites.
Y. Ogata, “On lewis’ simulation method for point processes,” Ieee Transactions On Information Theory , vol. 27, pp. 23–31, January 1981
1981
Cited alongside, same era.
Y. Ogata and H. Akaike, “On linear intensity models for mixed doubly stochastic poisson and self- exciting point processes,” Journal of the Royal Statistical Society. Series B (Methodological) , vol. 44, no. 1, pp. 102–107, Jan. 1982, ArticleType: research-article / Full publication date: 1982 / Copyright © 1982 Royal Statistical Society. [Online]. Available: http://www.jstor.org/stable/2984715
1982
Cited alongside, same era.
1988
Cited alongside, same era.
P. Brémaud and L. Massoulié, “Stability of nonlinear hawkes processes,” Annals of Probability , vol. 24, no. 3, pp. 1563–1588, 1996
1996
Cited alongside, same era.
P. Reynaud-Bouret and S. Schbath, “Adaptive estimation for hawkes processes; application to genome analysis,” Ann. Statist , vol. 38, pp. 2781–2822, 2010
2010
Later among the works it cites.
G. Mohler, M. Short, P. Brantingham, F. Schoenberg, and G. E. Tita, “Self-exciting point process modeling of crime,” Journal of the American Statistical Association , vol. 106, pp. 100–108, 2011
2011
Later among the works it cites.
P. Embrechts, T. Liniger, and L. Lu, “Multivariate hawkes processes: an application to financial data,” To appear in Journal of Applied Probability , 2011
2011
Later among the works it cites.
E. Bacry, K. Dayri, and J. Muzy, “Non-parametric kernel estimation for symmetric hawkes processes. application to high frequency financial data,” Eur. Phys. J. B , vol. 85, no. 5, p. 157, 2012. [Online]. Available: http://dx.doi.org/10.1140/epjb/e2012-21005-8
2012
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Y. Ogata, “Seismicity analysis through point-process modeling: A review,” Pure and Applied Geophysics , vol. 155, no. 2-4, pp. 471–507, Aug. 1999. [Online]. Available: http://www.springerlink.com/content/wqg0lxg6bmumaxmq/
1999
Cited alongside, same era.
A. Helmstetter and D. Sornette, “Subcritical and supercritical regimes in epidemic models of earthquake aftershocks,” Journal of geophysical research , vol. 107, no. B10, p. 2237, 2002
2002
Cited alongside, same era.
P. Hewlett, “Clustering of order arrivals, price impact and trade path optimisation,” in Workshop on Financial Modeling with Jump processes . Ecole Polytechnique, 2006
2006
Cited alongside, same era.
R. Crane and D. Sornette, “Robust dynamic classes revealed by measuring the response function of a social system,” Proceedings of the National Academy of Sciences , vol. 105, no. 41, pp. 15 649–15 653, 2008. [Online]. Available: http://www.pnas.org/content/105/41/15649.abstract
2008
Cited alongside, same era.
D. Marsan and O. Lengliné, “Extending earthquakes’ reach through cascading,” Science , vol. 319, p. 1076, 2008
2008
Cited alongside, same era.
L. Bauwens and N. Hautsch, Modelling financial high frequency data using point processes. , ser. In T. Mikosch, J-P. Kreiss, R. A. Davis, and T. G. Andersen, editors, Handbook of Financial Time Series. Springer Berlin Heidelberg, 2009
2009
Cited alongside, same era.
E. Lewis and G. Mohler, “A nonparametric em algorithm for multiscale hawkes processes,” Preprint , 2010
2010
Cited alongside, same era.
P. Reynaud-Bouret, V. Rivoirard, F. Grammont, and C. Tuleau-Malot, “Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis,” Hal e-print, 00789127, To appear in Journal of Mathematical Neuroscience
Cited in the paper.
J. Zhuang, D. Harte, M. Werner, S. Hainzl, and Z. S., “Basic models of seismicity: temporal models,” Community Online Resource for Statistical Seismicity Analysis, Available at http://www.corssa.org. , 2012
2012
Later among the works it cites.
E. Bacry and J. Muzy, “Hawkes model for price and trades high-frequency dynamics,” ArXiv e-prints , 2013
2013
Later among the works it cites.
E. Bacry, S. Delattre, M. Hoffmann, and J. F. Muzy, “Modelling microstructure noise with mutually exciting point processes,” Quantitative Finance , vol. 13, pp. 65–77, 2013
2013
Later among the works it cites.
S. Yang and H. Zha, “Mixture of mutually exciting processes for viral diffusion,” Proceedings of the 30 h t {}^{t}h International Conf. on Machine Learning , vol. 28, 2013
2013
Later among the works it cites.
S. J. Hardiman, N. Bercot, and J.-P. Bouchaud, “Critical reflexivity in financial markets: a Hawkes process analysis,” European Physical Journal B , vol. 86, p. 442, 2013
2013
Later among the works it cites.
E. Bacry, T. Jaisson, and J. Muzy, “ Estimation of slowly decreasing Hawkes kernels: Application to high frequency order book modelling,” ArXiv e-prints , 2014
2014
Closest in time.