Numerical method for means of linear Hawkes processes

References

• Balderama, E., F. P. Schoenberg, E. Murray, and P. W. Rundel. 2012. Application of branching point process models to the study of invasive red banana plants in Costa Rica. Journal of the American Statistical Association 107 (498):467–76. doi:10.1080/01621459.2011.641402.
   Web of Science ®Google Scholar
• Bacry, E., I. Mastromatteo, and J. F. Muzy. 2015. Hawkes processes in finance. arXiv 1502:04592v1.
   Google Scholar
• Bao, P., and X. X. Zhang. 2017. Uncovering and predicting the dynamic process of collective attention with survival theory. Scientific Reports 7 (1):2621. doi:10.1038/s41598-017-02826-6.
   PubMed Web of Science ®Google Scholar
• Chen, J., A. G. Hawkes, E. Scalas, and M. Trinh. 2018. Performance of information criteria for selection of Hawkes process models of financial data. Quantitative Finance 18 (2):225–35. doi:10.1080/14697688.2017.1403140.
   Web of Science ®Google Scholar
• Chen, S. Z., D. Witten, and A. Shojaie. 2017. Nearly assumptionless screening for the mutually-exciting multivariate Hawkes process. Electronic Journal of Statistics 11 (1):1207–34. doi:10.1214/17-EJS1251.
   PubMed Web of Science ®Google Scholar
• Cui, L. R., A. G. Hawkes, and H. Yi. 2020. An elementary derivation of moments of Hawkes processes. Advances in Applied Probability 52 (1). (accepted).
   Web of Science ®Google Scholar
• Cui, L. R., Z. L. Chen, and H. D. Gao. 2018. Reliability for systems with self-healing effect under shock models. Quality Technology & Quantitative Management 15 (5):551–67. doi:10.1080/16843703.2016.1264146.
   Web of Science ®Google Scholar
• Cui, L. R., Z. P. Li, and H. Yi. 2019. Partial self-exciting point processes and their parameter estimations. Communications in Statistics - Simulation and Computation 48 (10):2913–35. doi:10.1080/03610918.2018.1468463.
   Web of Science ®Google Scholar
• Dassios, A., and H. B. Zhao. 2011. A dynamic contagion process. Advances in Applied Probability 43 (3):814–46. doi:10.1239/aap/1316792671.
   Web of Science ®Google Scholar
• Dong, Q. L., L. R. Cui, and S. B. Si. 2020. Reliability and availability analysis of stochastic degradation systems based on bivariate Wiener processes. Applied Mathematical Modelling 79:414–433. doi:10.1016/j.apm.2019.10.044.
   Web of Science ®Google Scholar
• Duffie, D., D. Filipovic, and W. Schachermayer. 2003. Affine processes and applications in finance. The Annals of Applied Probability 13:984 1053. doi:10.1214/aoap/1060202833.
   Web of Science ®Google Scholar
• Ertekin, S., C. Rudin, and T. H. McCormick. 2015. Reactive point processes: A new approach to predicting power failures in underground electrical systems. The Annals of Applied Statistics 9 (1):122–44. doi:10.1214/14-AOAS789.
   Web of Science ®Google Scholar
• Fox, E. W., M. B. Short, F. P. Schoenberg, K. D. Coronges, and A. L. Bertozzi. 2016. Modeling E-mail networks and inferring leadership using self-exciting point processes. Journal of the American Statistical Association 514:564–84. doi:10.1080/01621459.2015.1135802.
   Web of Science ®Google Scholar
• Gao, X. F., and L. J. Zhu. 2018. Limit theorems for Markovian Hawkes processes with a large initial intensity. Stochastic Processes and Their Applications 128 (11):3807–39. doi:10.1016/j.spa.2017.12.001.
   Web of Science ®Google Scholar
• Hainaut, D., and S. Goutte. 2019. A switching microstructure model for stock prices. Mathematics and Financial Economics 13 (3):459–90. doi:10.1007/s11579-018-00234-6.
   Web of Science ®Google Scholar
• Halpin, P. F., and P. De Boeck. 2013. Modelling dyadic interaction with Hawkes processes. Psychometrika 78 (4):793–22. doi:10.1007/s11336-013-9329-1.
   PubMed Web of Science ®Google Scholar
• Hawkes, A. G. 1971a. Spectra of some self-exciting and mutually exciting point processes. Biometrika 58 (1):83–90. doi:10.1093/biomet/58.1.83.
   Web of Science ®Google Scholar
• Hawkes, A. G. 1971b. Point spectra of some mutually exciting point processes. Journal of the Royal Statistical Society: Series B (Methodological) 33:438–43. doi:10.1111/j.2517-6161.1971.tb01530.x.
   Web of Science ®Google Scholar
• Hegemann, R., E. Lewis, and A. Bertozzi. 2013. An “estimate & score algorithm” for simultaneous parameter estimation and reconstruction of missing data on social networks. Security Informatics 2 (1):14. doi:10.1186/2190-8532-2-1.
   Google Scholar
• Hu, W. S., and P. J. Jin. 2017. An adaptive Hawkes process formulation for estimating time-of-day zonal trip arrivals with location-based social networking check-in data. Transportation Research Part C: Emerging Technologies 79:136–55. doi:10.1016/j.trc.2017.02.002.
   Web of Science ®Google Scholar
• Jagielski, M., R. Kutner, and D. Sornette. 2017. Theory of earthquakes interevent times applied to financial markets. Physica A: Statistical Mechanics and Its Applications 483:68–73. doi:10.1016/j.physa.2017.04.115.
   Web of Science ®Google Scholar
• Jia, X. J., J. Y. Shen, and R. Xing. 2016. Reliability analysis for repairable multistate two-unit series systems when repair time can be neglected. IEEE Transactions on Reliability 65 (1):208–16. doi:10.1109/TR.2015.2461218.
   Web of Science ®Google Scholar
• Jia, X. J., J. Y. Shen, F. Q. Xu, R. H. Ma, and X. Y. Song. 2019. Modular decomposition signature for systems with sequential failure effect. Reliability Engineering & System Safety 189:435–44. doi:10.1016/j.ress.2019.05.003.
   Web of Science ®Google Scholar
• Baró, J. 2019. Topological properties of epidemic aftershock processes. arXiv 1908:03554v1.
   Google Scholar
• Krumin, M., I. Reutsky, and S. Shoham. 2010. Correlation-based analysis and generation of multiple spike trains using Hawkes models with an exogenous input. Frontiers in Computational Neuroscience 4:147. doi:10.3389/fncom.2010.00147.
   PubMed Web of Science ®Google Scholar
• Lewis, E., G. Mohler, P. J. Brantingham, and A. L. Bertozzi. 2012. Self-exciting point process models of civilian deaths in Iraq. Security Journal 25 (3):244–64. doi:10.1057/sj.2011.21.
   Web of Science ®Google Scholar
• Li, Z. P., L. R. Cui, and J. H. Chen. 2018. Traffic accident modeling via self-exciting point processes. Reliability Engineering & System Safety 180:312–20. doi:10.1016/j.ress.2018.07.035.
   Web of Science ®Google Scholar
• Lin, F.-C. 2011. A random effects epidemic-type aftershock sequence model. Computational Statistics & Data Analysis 55 (4):1610–6. doi:10.1016/j.csda.2010.09.031.
   PubMed Web of Science ®Google Scholar
• Likhyani, A., S. Bedathur, and P. Deepak. 2019. Location-specific influence quantification in location-based social networks. ACM Transactions on Intelligent Systems and Technology 10 (3):1–29. doi:10.1145/3300199.
   Web of Science ®Google Scholar
• Mohler, G. O., M. B. Short, P. J. Brantingham, F. P. Schoenberg, and G. E. Tita. 2011. Self-exciting point process modeling of crime. Journal of the American Statistical Association 106 (493):100–8. doi:10.1198/jasa.2011.ap09546.
   Web of Science ®Google Scholar
• Musmeci, F., and D. Vere-Jones. 1992. A space-time clustering model for historical earthquakes. Annals of the Institute of Statistical Mathematics 44 (1):1–11. doi:10.1007/BF00048666.
   Web of Science ®Google Scholar
• Ogata, Y. 1988. Statistical method for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association 401:9–27. doi:10.1080/01621459.1988.10478560.
   Web of Science ®Google Scholar
• Ross, S. M. 2014. Introduction to probability models. 11th ed.. USA: Elsevier.
   Google Scholar
• Reynaud-Bouret, P., and S. Schbath. 2010. Adaptive estimation for Hawkes processes: Application to genome analysis. The Annals of Statistics 38 (5):2781–822. doi:10.1214/10-AOS806.
   Web of Science ®Google Scholar
• Stehfest, H. 1970a. Algorithm 368 numerical inversion of Laplace transforms. Communications of the Acm 13 (1):47–9. doi:10.1145/361953.361969.
   Web of Science ®Google Scholar
• Stehfest, H. 1970b. Remark on Algorithm 368 numerical inversion of Laplace transforms. Communications of the Acm 13 (10):624–5. doi:10.1145/355598.362787.
   Web of Science ®Google Scholar
• Saichev, A., and D. Sornette. 2006. Renormalization of the ETAS branching model of triggered seismicity from total to observable seismicity. The European Physical Journal B 51 (3):443–59. doi:10.1140/epjb/e2006-00242-6.
   Web of Science ®Google Scholar
• Sornette, D., and M. J. Werner. 2005. Constraints on the Size of the smallest triggering earthquake from the ETAS model, Baath's law, and observed aftershock sequences. Journal of Geophysical Research 110 (B8):1–11. doi:10.1029/2004JB003535.
   Web of Science ®Google Scholar
• Vere-Jones, D., and T. Ozaki. 1982. Some examples of statistical estimation applied to earthquake data. Annals of the Institute of Statistical Mathematics 34 (1):189–207. doi:10.1007/BF02481022.
   Web of Science ®Google Scholar
• Zhu, L. 2013. Nonlinear Hawkes processes. PhD. Thesis., New York University.
   Google Scholar
• Zhuang, J. C., and J. Mateu. 2019. A semiparametric spatiotemporal Hawkes-type point process model with periodic background for crime data. Journal of the Royal Statistical Society: Series A (Statistics in Society) 182 (3):919–42. doi:10.1111/rssa.12429.
   Web of Science ®Google Scholar