markov property

in the following, $\text{[math]}$ is always a Polish space with Borel $\text{[math]}$ -algebra $\text{[math]}$ and $\text{[math]}$ is an $\text{[math]}$ -valued stochastic process. we assume that $\text{[math]}$ is a filtration generated by $\text{[math]}$ .
[cite:@klenke_prob_2020 section 17 markov chains]

we say that $\text{[math]}$ has the markov property if, for every $\text{[math]}$ and all $\text{[math]}$ with $\text{[math]}$ ,
$\text{[math]}$ [cite:@klenke_prob_2020 definition 17.1]