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Discrete minification processes and reversibility

Part of: Inference from stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

R. P. Littlejohn
R. P. Littlejohn*
Affiliation:
MAF Technology
*
∗ Postal address: MAF Technology, Invermay Agricultural Centre, Private Bag, Mosgiel, New Zealand.
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Abstract

Discrete minification processes are introduced and it is proved that the discrete first-order autoregression of McKenzie (1986) and the discrete minification process are mutually time-reversible if and only if they have common marginal geometric distribution, corresponding to a result for continuous processes given by Chernick et al. (1988). It is also proved that a discrete minification process is time-reversible if and only if it has marginal Bernoulli distribution.

Keywords

ALTERNATE PROBABILITY GENERATING FUNCTIONDISCRETE AUTOREGRESSIONGEOMETRIC PROCESSNON-GAUSSIAN TIME SERIESSELF-DECOMPOSABILITYTHINNINGTIME-REVERSIBILITY

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 62M10: Time series, auto-correlation, regression, etc.
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 82 - 91
Copyright
Copyright © Applied Probability Trust 1992 

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