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Stationary point processes by Markov-dependent intervals and infinite intensity

Published online by Cambridge University Press:  14 July 2016

D. J. Daley
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Abstract

Null-recurrent random walks with symmetric step distribution are mapped to give null-recurrent Markov chains on the interval (0, 1). These chains are used to construct stationary Wold processes (point processes with Markov-dependent intervals) with infinite intensity, which processes are simple (i.e., almost surely orderly) but not (analytically) orderly. As examples of point processes with infinite intensity, they are constructed without any intermediate step that relies on using point processes of finite intensity.

Keywords

WOLD PROCESSORDERLINESSKHINCHIN ORDERLINESSPOINT PROCESS WITH INFINITE INTENSITYTRANSFORMATION OF SYMMETRIC RANDOM WALKS
Type
Part 6 — Stochastic Processes
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 313 - 320
Copyright
Copyright © 1982 Applied Probability Trust 

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References

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