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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-4,
author = {Zbigniew S. Kowalski},
title = {An Application of Skew Product Maps to Markov Chains},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {55},
year = {2007},
pages = {35-41},
zbl = {1115.37001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-4}
}
Zbigniew S. Kowalski. An Application of Skew Product Maps to Markov Chains. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 35-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-4/