Cha\^{i}nes de Markov Constructives Index\'{e}es par Z
Jean Brossard, Christophe Leuridan

TL;DR
This paper investigates the conditions under which the innovations in a Markov chain fully determine the chain itself, and describes the missing information when they do not, within the context of constructive indexed Markov chains.
Contribution
It provides a necessary and sufficient condition for the innovations to completely determine the Markov chain and characterizes the missing information when this condition is not met.
Findings
Identifies when innovations fully determine the chain
Describes the structure of missing information
Provides theoretical conditions for Markov chain reconstruction
Abstract
Nous \'{e}tudions les cha\^{{\i}}nes de Markov gouvern\'{e}es par une relation de r\'{e}currence de la forme , o\`{u} est une suite de variables al\'{e}atoires ind\'{e}pendantes et de m\^{e}me loi telle pour tout , est ind\'{e}pendante de la suite . L'objet de l'article est de donner une condition n\'{e}cessaire et suffisante pour que les innovations d\'{e}terminent compl\`{e}tement la suite et de d\'{e}crire l'information manquante dans le cas contraire.
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