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A Markov construction for a multidimensional point process
Published online by Cambridge University Press: 14 July 2016
Abstract
A sequence of finite point processes {Pn } is constructed in 
using a Markov sequence of points. Essentially, in the process Pn consisting of n events, the coordinates of these events are simply the first n points of a Markov sequence suitably scaled so that the average density of the process is independent of n. The second-order properties of Pn are discussed and sufficient conditions are found for Pn to converge in distribution to a Poisson process as n →∞. A simple example involving the cardioid distribution is described.
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- Copyright © Applied Probability Trust 1977
References
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