Ordered thinnings of point processes and random measures

Fred Böker and Richard Serfozo

Stochastic Processes and their Applications, 1983, vol. 15, issue 2, 113-132

Abstract: 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.

Keywords: Point; process; random; measure; infinitely; divisible; process; thinning; compound; Poisson; process; Markov; chain (search for similar items in EconPapers)
Date: 1983
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Citations: View citations in EconPapers (2)

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