Rate of convergence to equilibrium of marked Hawkes processes

被引：30

作者：

Brémaud, P

Nappo, G

Torrisi, GL

机构：

[1] Ecole Normale Super, Dept Informat, F-75230 Paris 05, France

[2] EPFL, CH-1015 Lausanne, Switzerland

[3] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[4] CNR, Ist Applicaz Calcolo M Picone, I-00161 Rome, Italy

来源：

JOURNAL OF APPLIED PROBABILITY | 2002年 / 39卷 / 01期

关键词：

point processes; stochastic intensity; Hawkes processes; renewal theory; branching processes; convergence in variation; stochastic simulation;

D O I：

10.1017/S0021900200021562

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and nontrivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.

引用

页码：123 / 136

页数：14

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