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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

Information

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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