Random space change for multiparameter point processes

M. Gopalan Nair

doi:10.1214/aop/1176990743

Random space change for multiparameter point processes

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Abstract

A way of transforming a multiparameter point process into a Poisson process is given. As in the one-parameter case, the compensator characterization of the Poisson process plays an important role in random space change for the multiparameter point process. We use the characterization of planar Poisson processes in terms of the 1-compensator by Brown to derive random space-change theorems. The results obtained hold under weaker conditions than those in Merzbach and Nualart.

Original language	English
Pages (from-to)	1222-1231
Number of pages	10
Journal	The Annals of Probability
Volume	18
Issue number	3
DOIs	https://doi.org/10.1214/aop/1176990743
Publication status	Published - 1990
Externally published	Yes

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title = "Random space change for multiparameter point processes",

abstract = "A way of transforming a multiparameter point process into a Poisson process is given. As in the one-parameter case, the compensator characterization of the Poisson process plays an important role in random space change for the multiparameter point process. We use the characterization of planar Poisson processes in terms of the 1-compensator by Brown to derive random space-change theorems. The results obtained hold under weaker conditions than those in Merzbach and Nualart.",

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T1 - Random space change for multiparameter point processes

AU - Nair, M. Gopalan

PY - 1990

Y1 - 1990

N2 - A way of transforming a multiparameter point process into a Poisson process is given. As in the one-parameter case, the compensator characterization of the Poisson process plays an important role in random space change for the multiparameter point process. We use the characterization of planar Poisson processes in terms of the 1-compensator by Brown to derive random space-change theorems. The results obtained hold under weaker conditions than those in Merzbach and Nualart.

AB - A way of transforming a multiparameter point process into a Poisson process is given. As in the one-parameter case, the compensator characterization of the Poisson process plays an important role in random space change for the multiparameter point process. We use the characterization of planar Poisson processes in terms of the 1-compensator by Brown to derive random space-change theorems. The results obtained hold under weaker conditions than those in Merzbach and Nualart.

KW - Point process Poisson process compensator stopping set random space change

U2 - 10.1214/aop/1176990743

DO - 10.1214/aop/1176990743

M3 - Article

SN - 0091-1798

VL - 18

SP - 1222

EP - 1231

JO - The Annals of Probability

JF - The Annals of Probability

IS - 3

ER -

Random space change for multiparameter point processes

Abstract

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