# A note on Markov operators and transition systems

Colloquium Mathematicae (2002)

- Volume: 91, Issue: 2, page 183-190
- ISSN: 0010-1354

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topBartosz 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 -

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