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A class of interacting marked point processes: rate of convergence to equilibrium

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

G. L. Torrisi
G. L. Torrisi*
Affiliation:
Istituto per le Applicazioni del Calcolo, Roma
*
∗ Postal address: Istituto per le Applicazioni del Calcolo ‘M. Picone’ (IAC-CNR), Viale del Policlinico 137, 00161 Roma, Italy. Email address: torrisi@iac.rm.cnr.it
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Abstract

In this paper we obtain the rate of convergence to equilibrium of a class of interacting marked point processes, introduced by Kerstan, in two different situations. Indeed, we prove the exponential and subexponential ergodicity of such a class of stochastic processes. Our results are an extension of the corresponding results of Brémaud, Nappo and Torrisi. The generality of the dynamics which we take into account allows the application to the so-called loss networks, and multivariate birth and death processes.

Keywords

Point processesstochastic intensityergodicityHawkes processesloss networksbirth and death processes

MSC classification

Primary: 60G55: Point processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 137 - 160
Copyright
Copyright © Applied Probability Trust 2002 

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