A note on Markov operators and transition systems
Tom 91 / 2002
Colloquium Mathematicum 91 (2002), 183-190
MSC: 37A30, 37B50.
DOI: 10.4064/cm91-2-3
Streszczenie
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.
