Bulletin of the Belgian Mathematical Society - Simon Stevin

Some non asymptotic tail estimates for Hawkes processes

Patricia Reynaud-Bouret and Emmanuel Roy

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Abstract

We use the Poisson cluster process structure of a Hawkes process to derive non asymptotic estimates of the tail of the extinction time, of the coupling time or of the number of points per interval. This allows us to define a family of independent Hawkes processes; each of them approximating the initial process on a particular interval. Then we can easily derive exponential inequalities for Hawkes processes which can precise the ergodic theorem.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 13, Number 5 (2007), 883-896.

Dates
First available in Project Euclid: 1 February 2007

Permanent link to this document
http://projecteuclid.org/euclid.bbms/1170347811

Mathematical Reviews number (MathSciNet)
MR2293215

Zentralblatt MATH identifier
1120.60052

Subjects
Primary: 60G55: Point processes

Keywords
Point processes exponential inequalities approximate simulation of a stationary Hawkes process

Citation

Reynaud-Bouret, Patricia; Roy, Emmanuel. Some non asymptotic tail estimates for Hawkes processes. Bull. Belg. Math. Soc. Simon Stevin 13 (2007), no. 5, 883--896. http://projecteuclid.org/euclid.bbms/1170347811.


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