A note on Markov operators and transition systems

Bartosz Frej. "A note on Markov operators and transition systems." Colloquium Mathematicae 91.2 (2002): 183-190. <http://eudml.org/doc/283599>.

@article{BartoszFrej2002,
abstract = {On a compact metric space X one defines a transition system to be a lower semicontinuous map $X → 2^\{X\}$. 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.},
author = {Bartosz Frej},
journal = {Colloquium Mathematicae},
keywords = {Markov operator; transition probability; transition system},
language = {eng},
number = {2},
pages = {183-190},
title = {A note on Markov operators and transition systems},
url = {http://eudml.org/doc/283599},
volume = {91},
year = {2002},
}

TY - JOUR
AU - Bartosz Frej
TI - A note on Markov operators and transition systems
JO - Colloquium Mathematicae
PY - 2002
VL - 91
IS - 2
SP - 183
EP - 190
AB - On a compact metric space X one defines a transition system to be a lower semicontinuous map $X → 2^{X}$. 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.
LA - eng
KW - Markov operator; transition probability; transition system
UR - http://eudml.org/doc/283599
ER -