Geodesic
A note on Markov operators and transition systems
Bartosz Frej1
1 Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Colloquium Mathematicum, Tome 91 (2002) no. 2, pp. 183-190.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

On a compact metric space $X$ one defines a transition system to be a lower semicontinuous map $X\to 2^X$. It is known that every Markov operator on $C(X)$ induces a transition system on $X$ and that commuting of Markov operators implies commuting of the induced transition systems. We show that even in finite spaces a pair of commuting transition systems may not be induced by commuting Markov operators. The existence of trajectories for a pair of transition systems or Markov operators is also investigated.
DOI : 10.4064/cm91-2-3
Keywords: compact metric space defines transition system lower semicontinuous map known every markov operator induces transition system commuting markov operators implies commuting induced transition systems even finite spaces pair commuting transition systems may induced commuting markov operators existence trajectories pair transition systems markov operators investigated

Bartosz Frej 1

1 Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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Bartosz Frej. A note on Markov operators and transition systems. Colloquium Mathematicum, Tome 91 (2002) no. 2, pp. 183-190. doi : 10.4064/cm91-2-3. http://geodesic.mathdoc.fr/articles/10.4064/cm91-2-3/

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