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Thinning of point processes—covariance analyses
Published online by Cambridge University Press: 01 July 2016
Abstract
Cross-covariances between the Bernoulli thinned processes of an arbitrary point process are determined. When the point process is renewal it is shown that zero correlation implies independence. An example is given to show that zero covariance between intervals does not imply zero covariance between counts. Mark-dependent thinning of Markov renewal processes is discussed and the results are applied to the overflow queue. Here we give an example of two uncorrelated but dependent renewal processes, neither of which is Poisson, which yield a Poisson process when superposed. Finally, we study Markov-chain thinning of renewal processes.
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- Copyright © Applied Probability Trust 1985
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