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Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance.
Billingsley, PatrickP. (1968). Convergence of Probability Measures. Wiley, New York
1968
Earlier work this paper cites.
Hawkes, Alan G.A. G. (1971). Point spectra of some mutually exciting point processes. J. R. Stat. Soc. Ser. B Stat. Methodol. 33 438–443
1971
Earlier work this paper cites.
Hawkes, Alan G.A. G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika 58 83–90
1971
Earlier work this paper cites.
Hawkes, Alan G.A. G. andOakes, DavidD. (1974). A cluster process representation of a self-exciting process. J. Appl. Probab. 11 493–503
1974
Earlier work this paper cites.
Jacod, JeanJ. (1974/75). Multivariate point processes: Predictable projection, Radon–Nikodým derivatives, representation of martingales. Z. Wahrsch. Verw. Gebiete 31 235–253
1974
Earlier work this paper cites.
Petrov, V. V.V. V. (1975). Sums of Independent Random Variables. Springer, New York
1975
Earlier work this paper cites.
Adamopoulos, L.L. (1976). Cluster models for earthquakes: Regional comparisons. Journal of the International Association for Mathematical Geology 8 463–475
1976
Earlier work this paper cites.
Ogata, YosihikoY. (1978). The asymptotic behaviour of maximum likelihood estimators for stationary point processes. Ann. Inst. Statist. Math. 30 243–261
1978
Earlier work this paper cites.
Ogata, YoshihikoY. (1983). Likelihood analysis of point processes and its applications to seismological data. Bull. Inst. Internat. Statist. 50 943–961
1983
Earlier work this paper cites.
Cox, J. C.J. C., IngersollJr, J. E.J. E. andRoss, S. A.S. A. (1985). A theory of the term structure of interest rates. Econometrica
1985
Earlier work this paper cites.
Jacod, JeanJ. andShiryaev, Albert N.A. N. (1987). Limit Theorems for Stochastic Processes. Grundlehren der Mathematischen Wissenschaften 288. Springer, Berlin
1987
Earlier work this paper cites.
Daley, D. J.D. J. andVere-Jones, D.D. (1988). An Introduction to the Theory of Point Processes. Springer, New York
1988
Earlier work this paper cites.
Jakubowski, A.A., Mémin, J.J. andPagès, G.G. (1989). Convergence en loi des suites d’intégrales stochastiques sur l’espace 𝐃 1 \mathbf{D}^{1} de Skorokhod. Probab. Theory Related Fields 81 111–137
1989
Earlier work this paper cites.
Kurtz, Thomas G.T. G. andProtter, PhilipP. (1991). Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab. 19 1035–1070
1991
Earlier work this paper cites.
Heston, S. L.S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies 6 327–343
1993
Cited alongside, same era.
Kalashnikov, VladimirV. (1997). Geometric Sums: Bounds for Rare Events with Applications: Risk Analysis, Reliability, Queueing. Mathematics and Its Applications 413. Kluwer, Dordrecht
1997
Cited alongside, same era.
Brémaud, PierreP. andMassoulié, LaurentL. (2001). Hawkes branching point processes without ancestors. J. Appl. Probab. 38 122–135
2001
Cited alongside, same era.
Bauwens, L.L. andHautsch, N.N. (2004). Dynamic latent factor models for intensity processes. Working paper, UCL-CORE Center for Operations Research and Econometrics
2004
Cited alongside, same era.
Bouchaud, J.-P.J.-P., Gefen, Y.Y., Potters, M.M. andWyart, M.M. (2004). Fluctuations and response in financial markets: The subtle nature of “random” price changes. Quant. Finance 4 176–190
Barczy, M.M., Ispány, M.M. andPap, G.G. (2011). Asymptotic behavior of unstable INAR ( p ) \mathrm{INAR}(p) processes. Stochastic Process. Appl. 121 583–608
2011
Later among the works it cites.
Embrechts, PaulP., Liniger, ThomasT. andLin, LuL. (2011). Multivariate Hawkes processes: An application to financial data. J. Appl. Probab. 48A 367–378
2011
Later among the works it cites.
Alaya, Mohamed BenM. B. andKebaier, AhmedA. (2012). Parameter estimation for the square-root diffusions: Ergodic and nonergodic cases. Stoch. Models 28 609–634
2012
Later among the works it cites.
Bacry, E.E., Dayri, K.K. andMuzy, J.-F.J.-F. (2012). Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data. Eur. Phys. J. B 85 1–12
2012
Later among the works it cites.
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2004
Cited alongside, same era.
Lillo, F.F. andFarmer, J. D.J. D. (2004). The long memory of the efficient market. Stud. Nonlinear Dyn. Econom. 8 3
2004
Cited alongside, same era.
Chavez-Demoulin, V.V., Davison, A. C.A. C. andMcNeil, A. J.A. J. (2005). Estimating value-at-risk: A point process approach. Quant. Finance 5 227–234
2005
Cited alongside, same era.
Hewlett, P.P. (2006). Clustering of order arrivals, price impact and trade path optimisation. In Workshop on Financial Modeling with Jump Processes, 6–8 September 2006. Ecole Polytechnique, France
2006
Cited alongside, same era.
Bowsher, Clive G.C. G. (2007). Modelling security market events in continuous time: Intensity based, multivariate point process models. J. Econometrics 141 876–912
2007
Cited alongside, same era.
Large, J.J. (2007). Measuring the resiliency of an electronic limit order book. Journal of Financial Markets 10 1–25
2007
Cited alongside, same era.
Wyart, M.M., Bouchaud, J.-P.J.-P., Kockelkoren, J.J., Potters, M.M. andVettorazzo, M.M. (2008). Relation between bid–ask spread, impact and volatility in order-driven markets. Quant. Finance 8 41–57
2008
Cited alongside, same era.
Aït-Sahalia, Y.Y., Cacho-Diaz, J.J. andLaeven, R. J.R. J. (2010). Modeling financial contagion using mutually exciting jump processes. Technical report, National Bureau of Economic Research, Cambridge, MA
2010
Cited alongside, same era.
2012
Later among the works it cites.
Filimonov, V.V. andSornette, D.D. (2012). Quantifying reflexivity in financial markets: Toward a prediction of flash crashes. Phys. Rev. E (3) 85 056108
2012
Later among the works it cites.
Bacry, E.E., Delattre, S.S., Hoffmann, M.M. andMuzy, J. F.J. F. (2013). Modelling microstructure noise with mutually exciting point processes. Quant. Finance 13 65–77
2013
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2013
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2013
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2013
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Jaisson, T.T. (2013). Market impact as anticipation of the order flow imbalance. Working paper
2013
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Shah, P. V.P. V. andJana, R. K.R. K. (2013). Results on generalized Mittag–Leffler function via Laplace transform. Appl. Math. Sci. (Ruse) 7 567–570
2013
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Zhu, LingjiongL. (2013). Central limit theorem for nonlinear Hawkes processes. J. Appl. Probab. 50 760–771
2013
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Jaisson, T.T. andRosenbaum, M.M. (2014). Limit theorems for nearly unstable Hawkes processes: Version with technical appendix. Technical Report 1607, Laboratoire de Probabilités et Modèles Aléatoires, Univ. Pierre et Marie Curie
2014
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