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On the fluctuation of stochastically monotone Markov chains and some applications

Published online by Cambridge University Press:  14 July 2016

Harry Cohn
Harry Cohn*
Affiliation:
University of Melbourne
*
∗ Postal address: Department of Statistics, University of Melbourne, Richard Berry Building, Parkville, VIC 3052, Australia.
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Abstract

A Borel–Cantelli-type property in terms of one-step transition probabilities is given for events like {|Xn+1| > a + ε, |Xn|≦a}, a and ε being two positive numbers. Applications to normed sums of i.i.d. random variables with infinite mean and branching processes in varying environment with or without immigration are derived.

Keywords

STOCHASTIC MONOTONICITYCREEPINGJUMPINGINFINITE MEANINDEPENDENCERELATIVE STABILITYVARYING ENVIRONMENTIMMIGRATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 178 - 184
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

Research partially carried out while the author was at the University of California, San Diego.

References

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