Editing Markov chain (section)

==== Terminology ====
Some authors call any irreducible, positive recurrent Markov chains ergodic, even periodic ones.<ref>{{cite book |last1=Parzen |first1=Emanuel |title=Stochastic Processes |date=1962 |publisher=Holden-Day |isbn=0-8162-6664-6 |location=San Francisco |page=145}}</ref> In fact, merely irreducible Markov chains correspond to [[ergodicity|ergodic processes]], defined according to [[ergodic theory]].<ref name=":2" />

Some authors call a matrix ''primitive'' if there exists some integer <math>k</math> such that all entries of <math>M^k</math> are positive.<ref>{{Cite book |last=Seneta |first=E. (Eugene) |url=http://archive.org/details/nonnegativematri00esen_0 |title=Non-negative matrices; an introduction to theory and applications |date=1973 |publisher=New York, Wiley |others=Internet Archive |isbn=978-0-470-77605-6}}</ref> Some authors call it ''regular''.<ref>{{Cite web |date=2020-03-22 |title=10.3: Regular Markov Chains |url=https://math.libretexts.org/Bookshelves/Applied_Mathematics/Applied_Finite_Mathematics_(Sekhon_and_Bloom)/10%3A_Markov_Chains/10.03%3A_Regular_Markov_Chains |access-date=2024-02-01 |website=Mathematics LibreTexts |language=en}}</ref>