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A transition matrix is a square matrix used to describe the transitions of a Markov chain.

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How to understand the definition of Markov Chain $P(X_{n+1}\in B\mid \mathcal{F}_n)=p(X_n,B)$?

The definition of Markov Chain in Durrett (Probability: Theory and Examples, 2019, Section 5.2) is: $$P(X_{n+1}\in B\mid \mathcal{F}_n)=p(X_n,B), $$ where $p$ is the Markov transition kernel distribut …