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Criteria for the non-ergodicity of stochastic processes: application to the exponential back-off protocol

Published online by Cambridge University Press:  14 July 2016

Guy Fayolle  and
Rudolph Iasnogorodski
Guy Fayolle*
Affiliation:
INRIA
Rudolph Iasnogorodski*
Affiliation:
Université d'Orléans
*
∗Postal address: INRIA, Domaine de Voluceau — Rocquencourt, BP 105, 78153Le Chesnay Cedex, France.
∗∗Postal address: Département de Mathématiques, Université d'Orléans, 45046 Orléans la Source, France.
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Abstract

In this paper, we present some simple new criteria for the non-ergodicity of a stochastic process (Yn), n ≧ 0 in discrete time, when either the upward or downward jumps are majorized by i.i.d. random variables. This situation is encountered in many practical situations, where the (Yn) are functionals of some Markov chain with countable state space. An application to the exponential back-off protocol is described.

Keywords

ERGODICITYSUBMARTINGALES
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 347 - 354
Copyright
Copyright © Applied Probability Trust 1987 

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References

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