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Conditionally Independent Increment Point Processes

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Ricardo Vélez Ibarrola  and
Tomás Prieto-Rumeau
Ricardo Vélez Ibarrola*
Affiliation:
Universidad Nacional de Educación a Distancia
Tomás Prieto-Rumeau*
Affiliation:
Universidad Nacional de Educación a Distancia
*
∗Postal address: Departamento de Estadística, Universidad Nacional de Educación a Distancia (UNED), Calle Senda del Rey 9, 28040 Madrid, Spain.
∗Postal address: Departamento de Estadística, Universidad Nacional de Educación a Distancia (UNED), Calle Senda del Rey 9, 28040 Madrid, Spain.
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Abstract

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In this paper we introduce conditionally independent increment point processes, that is, processes that are conditionally independent inside and outside a bounded set A given N(A), the number of points in A. We show that these point processes can be characterized by means of the avoidance function of a multinomial ‘support process’, the solution of a suitably defined linear system of equations, and, finally, the infinitesimal matrix of a continuous-time Markov chain.

Keywords

Markov and multinomial point processescontinuous-time Markov chain

MSC classification

Secondary: 60G55: Point processes 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 2 , June 2011 , pp. 490 - 513
Copyright
Copyright © Applied Probability Trust 2011 

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