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March 2015 The Hawkes process with different exciting functions and its asymptotic behavior
Raúl Fierro, Víctor Leiva, Jesper Møller
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J. Appl. Probab. 52(1): 37-54 (March 2015). DOI: 10.1239/jap/1429282605

Abstract

The standard Hawkes process is constructed from a homogeneous Poisson process and uses the same exciting function for different generations of offspring. We propose an extension of this process by considering different exciting functions. This consideration may be important in a number of fields; e.g. in seismology, where main shocks produce aftershocks with possibly different intensities. The main results are devoted to the asymptotic behavior of this extension of the Hawkes process. Indeed, a law of large numbers and a central limit theorem are stated. These results allow us to analyze the asymptotic behavior of the process when unpredictable marks are considered.

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Raúl Fierro. Víctor Leiva. Jesper Møller. "The Hawkes process with different exciting functions and its asymptotic behavior." J. Appl. Probab. 52 (1) 37 - 54, March 2015. https://doi.org/10.1239/jap/1429282605

Information

Published: March 2015
First available in Project Euclid: 17 April 2015

zbMATH: 1315.60055
MathSciNet: MR3336845
Digital Object Identifier: 10.1239/jap/1429282605

Subjects:
Primary: 60G55
Secondary: 60F05

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 1 • March 2015
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