Ordered thinnings of point processes and random measures
This is a study of thinnings of point processes and random measures on the real line that satisfy a weak law of large numbers. The thinning procedures have dependencies based on the order of the points or masses being thinned such that the thinned process is a composition of two random measures. It is shown that the thinned process (normalized by a certain function) converges in distribution if and only if the thinning process does. This result is used to characterize the convergence of thinned processes to infinitely divisible processes, such as a compound Poisson process, when the thinning is independent and nonhomogeneous, stationary, Markovian, or regenerative. Thinning by a sequence of independent identically distributed operations is also discussed. The results here contain Renyi's classical thinning theorem and many of its extensions.
Year of publication: |
1983
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Authors: | Böker, Fred ; Serfozo, Richard |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 15.1983, 2, p. 113-132
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Publisher: |
Elsevier |
Keywords: | Point process random measure infinitely divisible process thinning compound Poisson process Markov chain |
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