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Poisson convergence for point processes on the plane

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  09 April 2009

B. Gail Ivanoff
B. Gail Ivanoff
Affiliation:
Department of MathematicsUniversity of OttawaOttawa, Ontario K1N 9B4, Canada
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Abstract

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A compensator is defined for a point process in two dimensions. It is shown that a Poisson process is characterized by a continuous deterministic compensator. Sufficient conditions are given for convergence in distribution of a sequence of two-dimensional point processes in the Skorokhod topology to a Poisson process when the corresponding sequence of compensators converges pointwise in probability to a continuous deterministic function.

Keywords

simple point processSkorokhod function spaceweak martingalestrong martingaleweak submartingalestrong submartingaleincreasing processcompensator.

MSC classification

Secondary: 60G55: Point processes 60F17: Functional limit theorems; invariance principles 60G48: Generalizations of martingales
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 2 , October 1985 , pp. 253 - 269
Copyright
Copyright © Australian Mathematical Society 1985

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