Transition probability functions can always be used to generate Markov operators, correct? So is it correct to say that a Markov process is a collection of Markov operators? On the other hand, are there Markov operators NOT generated by transition probability functions?
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I thought there was a 1-1 correspondence between markov operators and markov transition kernels given by $P(x,A) \mapsto \mathcal{P}\mathbb{1}_A(x)$ but I'm not sure why we care about these as two separate objects in that case – iYOA Apr 26 '20 at 19:00