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Noncausality and Marginalization of Markov Processes

Published online by Cambridge University Press:  11 February 2009

J.P. Florens ,
M. Mouchart  and
J.M. Rolin
J.P. Florens
Affiliation:
Université des Sciences Sociales
M. Mouchart
Affiliation:
Université Catholique de Louvain
J.M. Rolin
Affiliation:
Université Catholique de Louvain
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Abstract

In this paper it is shown that a subprocess of a Markov process is markovian if a suitable condition of noncausality is satisfied. Furthermore, a markovian condition is shown to be a natural condition when analyzing the role of the horizon (finite or infinite) in the property of noncausality. We also give further conditions implying that a process is both jointly and marginally markovian only if there is both finite and infinite noncausality and that a process verifies both finite and infinite noncausality only if it is markovian. Counterexamples are also given to illustrate the cases where these further conditions are not satisfied.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 2 , April 1993 , pp. 241 - 262
Copyright
Copyright © Cambridge University Press 1993

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