An Application of Skew Product Maps to Markov Chains
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 35-41
MSC: Primary 37A05; Secondary 60J10.
DOI: 10.4064/ba55-1-4
Abstract
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.
