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November 1996 Some monotonicity and dependence properties of self-exciting point processes
Andrzej Kwieciński, Ryszard Szekli
Ann. Appl. Probab. 6(4): 1211-1231 (November 1996). DOI: 10.1214/aoap/1035463329

Abstract

Point processes on the positive real axis which are positively self-exciting in a sense expressed by their martingale dynamics are studied in this paper. It is shown that such processes can be realized as increasing mappings of Poisson processes and are therefore associated in appropriate manners. Some examples are presented, including Hawkes, renewal, Pólya-Lundberg, Markov dependent, semi-Markov, in addition to other point processes. As corollaries an extension of the Burton-Waymire association result and a solution of the Glasserman conjecture are obtained. Some results on dependence in stochastic processes of interest in queueing are given as a by product.

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Andrzej Kwieciński. Ryszard Szekli. "Some monotonicity and dependence properties of self-exciting point processes." Ann. Appl. Probab. 6 (4) 1211 - 1231, November 1996. https://doi.org/10.1214/aoap/1035463329

Information

Published: November 1996
First available in Project Euclid: 24 October 2002

zbMATH: 1002.60538
MathSciNet: MR1422983
Digital Object Identifier: 10.1214/aoap/1035463329

Subjects:
Primary: 60G55
Secondary: 60K25

Keywords: association , compensator , self-exciting point process , Stochastic intensity

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 4 • November 1996
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