Bordenave, Charles; Torrisi, Giovanni Luca Large deviations of Poisson cluster processes. (English) Zbl 1152.60316 Stoch. Models 23, No. 4, 593-625 (2007). Summary: We prove scalar and sample path large deviation principles for a large class of Poisson cluster processes. As a consequence, we provide a large deviation principle for ergodic Hawkes point processes. Cited in 1 ReviewCited in 46 Documents MSC: 60F10 Large deviations 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) Keywords:Hawkes processes; large deviations; Poisson cluster processes; Poisson processes PDFBibTeX XMLCite \textit{C. Bordenave} and \textit{G. L. Torrisi}, Stoch. Models 23, No. 4, 593--625 (2007; Zbl 1152.60316) Full Text: DOI arXiv References: [1] DOI: 10.1137/1112074 · Zbl 0178.20004 · doi:10.1137/1112074 [2] DOI: 10.1214/aop/1065725193 · Zbl 0870.60043 · doi:10.1214/aop/1065725193 [3] DOI: 10.1239/aap/1134587756 · Zbl 1102.60030 · doi:10.1239/aap/1134587756 [4] DOI: 10.1239/jap/1019737993 · Zbl 1005.60062 · doi:10.1239/jap/1019737993 [5] DOI: 10.1002/1521-4036(200201)44:1<83::AID-BIMJ83>3.0.CO;2-W · Zbl 1052.62111 · doi:10.1002/1521-4036(200201)44:1<83::AID-BIMJ83>3.0.CO;2-W [6] DOI: 10.1080/14697680500039613 · Zbl 1118.91353 · doi:10.1080/14697680500039613 [7] Daley D.J., An Introduction to the Theory of Point Processes,, 2. ed. (2003) · Zbl 1026.60061 [8] DOI: 10.1016/0304-4149(94)90020-5 · Zbl 0805.60020 · doi:10.1016/0304-4149(94)90020-5 [9] Dembo A., Large Deviations Techniques and Applications,, 2. ed. (1998) · Zbl 0896.60013 [10] Ganesh A., Electron. J. Probab. 10 pp 1026– (2005) [11] Gusto G., Stat. Appl. Genet. Mol. Biol. 4 (2005) [12] DOI: 10.1093/biomet/58.1.83 · Zbl 0219.60029 · doi:10.1093/biomet/58.1.83 [13] Hawkes A.G., J. Roy. Statist. Soc. Ser. B 33 pp 438– (1971) [14] DOI: 10.2307/3212693 · Zbl 0305.60021 · doi:10.2307/3212693 [15] Jagers P., Branching Processes with Biological Applications (1975) · Zbl 0356.60039 [16] DOI: 10.1007/BF00161089 · Zbl 05473260 · doi:10.1007/BF00161089 [17] DOI: 10.1016/S0304-4149(98)00006-4 · Zbl 0944.60053 · doi:10.1016/S0304-4149(98)00006-4 [18] Mler J., Highly Structured Stochastic Systems pp 264– (2003) [19] DOI: 10.1239/aap/1059486821 · Zbl 1045.60007 · doi:10.1239/aap/1059486821 [20] DOI: 10.1239/aap/1127483739 · Zbl 1074.60057 · doi:10.1239/aap/1127483739 [21] DOI: 10.1239/aap/1113402399 · Zbl 1078.60012 · doi:10.1239/aap/1113402399 [22] DOI: 10.1016/j.spl.2007.01.007 · Zbl 1117.60052 · doi:10.1016/j.spl.2007.01.007 [23] Mler J., Statistical Inference and Simulation for Spatial Point Processes (2004) [24] Neyman J., J. R. Statist. Soc. B 20 pp 1– (1958) [25] DOI: 10.2307/2288914 · doi:10.2307/2288914 [26] DOI: 10.1023/A:1003403601725 · Zbl 0947.62061 · doi:10.1023/A:1003403601725 [27] Ogata Y., J. R. Statist. Soc. B 44 pp 102– (1982) [28] Reynaud-Bouret P., Bull. Belg. Math. Soc. Simon Stevin 13 pp 883– (2007) [29] DOI: 10.1239/jap/1019737994 · Zbl 1009.60041 · doi:10.1239/jap/1019737994 [30] DOI: 10.1007/BF02481022 · doi:10.1007/BF02481022 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.