AN ELEMENTARY DERIVATION OF MOMENTS OF HAWKES PROCESSES
Hawkes processes have been widely used in many areas, but their probability properties can be quite difficult. In this paper an elementary approach is presented to obtain moments of Hawkes processes and/or the intensity of a number of marked Hawkes processes, in which the detailed outline is given s...
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| Published in | Advances in applied probability Vol. 52; no. 1; pp. 102 - 137 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Sheffield
Applied Probability Trust
01.03.2020
Cambridge University Press |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0001-8678 1475-6064 1475-6064 |
| DOI | 10.1017/apr.2019.53 |
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| Abstract | Hawkes processes have been widely used in many areas, but their probability properties can be quite difficult. In this paper an elementary approach is presented to obtain moments of Hawkes processes and/or the intensity of a number of marked Hawkes processes, in which the detailed outline is given step by step; it works not only for all Markovian Hawkes processes but also for some non-Markovian Hawkes processes. The approach is simpler and more convenient than usual methods such as the Dynkin formula and martingale methods. The method is applied to one-dimensional Hawkes processes and other related processes such as Cox processes, dynamic contagion processes, inhomogeneous Poisson processes, and non-Markovian cases. Several results are obtained which may be useful in studying Hawkes processes and other counting processes. Our proposed method is an extension of the Dynkin formula, which is simple and easy to use. |
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| AbstractList | Hawkes processes have been widely used in many areas, but their probability properties can be quite difficult. In this paper an elementary approach is presented to obtain moments of Hawkes processes and/or the intensity of a number of marked Hawkes processes, in which the detailed outline is given step by step; it works not only for all Markovian Hawkes processes but also for some non-Markovian Hawkes processes. The approach is simpler and more convenient than usual methods such as the Dynkin formula and martingale methods. The method is applied to one-dimensional Hawkes processes and other related processes such as Cox processes, dynamic contagion processes, inhomogeneous Poisson processes, and non-Markovian cases. Several results are obtained which may be useful in studying Hawkes processes and other counting processes. Our proposed method is an extension of the Dynkin formula, which is simple and easy to use. |
| Author | HAWKES, ALAN CUI, LIRONG YI, HE |
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| Cites_doi | 10.1137/090771272 10.1198/jasa.2011.ap09546 10.1080/03610918.2018.1468463 10.2307/3212408 10.1198/016214508000000148 10.1007/s007800200079 10.1016/j.ress.2018.07.035 10.1111/j.2517-6161.1955.tb00188.x 10.1080/14697688.2017.1403140 10.1239/aap/1059486821 10.2307/3212693 10.1080/01621459.1988.10478560 10.2307/3212409 10.1111/j.2517-6161.1984.tb01308.x 10.1239/aap/1019160957 10.1093/biomet/58.1.83 10.1239/aap/1316792671 10.1080/16843703.2016.1264146 10.1287/stsy.2018.0014 10.1214/aoap/1060202833 10.1111/j.2517-6161.1971.tb01530.x |
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| Title | AN ELEMENTARY DERIVATION OF MOMENTS OF HAWKES PROCESSES |
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