A note on Markov operators and transition systems
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.
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
Affiliations des auteurs :
Bartosz Frej 1
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author = {Bartosz Frej},
title = {A note on {Markov} operators and transition systems},
journal = {Colloquium Mathematicum},
pages = {183--190},
publisher = {mathdoc},
volume = {91},
number = {2},
year = {2002},
doi = {10.4064/cm91-2-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm91-2-3/}
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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
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