An Application of Skew Product Maps to Markov Chains
By using the skew product definition of a Markov chain we obtain the following results:
(a) Every $k$-step Markov chain is a quasi-Markovian process.
(b) Every piecewise linear map with a Markovian partition defines a Markov chain for every absolutely continuous invariant measure.(c) Satisfying the Chapman–Kolmogorov equation is not sufficient for a process to be quasi-Markovian.