Talk:Markov chains on a measurable state space

Statistics Low‑importance

	This article is within the scope of WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.StatisticsWikipedia:WikiProject StatisticsTemplate:WikiProject StatisticsStatistics articles
Low	This article has been rated as Low-importance on the importance scale.

Mathematics Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

Articles for creation

	This article was reviewed by member(s) of WikiProject Articles for creation. The project works to allow users to contribute quality articles and media files to the encyclopedia and track their progress as they are developed. To participate, please visit the project page for more information.Articles for creationWikipedia:WikiProject Articles for creationTemplate:WikiProject Articles for creationAfC articles
	This article was accepted from this draft on 4 November 2015 by reviewer Wikiisawesome (talk · contribs).

Merger with Harris chain

Based on the current state of the article, it looks like Harris Chain and Markov chains on a measurable state space are synonyms, but I do not have the relevant mathematical knowledge. Is there any reason to have two different articles, or should those be merged? If not, could someone provide a description of how the two concepts differ? 7804j (talk) 15:13, 4 December 2019 (UTC)[reply]

No. Harris chain is a special case of a Markov chain on a measurable state space. For example, try the (highly degenerate) process that, being at a point x of the real line, just jumps to x+1 (with probability 1). This process is not a Harris chain (and not regenerative), but still, is a Markov chain on a measurable state space. Roughly, it never forgets its past; a Harris process must forget (gradually, ultimately). Boris Tsirelson (talk) 18:37, 4 December 2019 (UTC)[reply]

Addition of non-time-homogeneous case

Since the page is not specified to be time-homogeneous only and there are cases where such processes are indeed relevant, I don't see the problem of adding this generalisation to the definition. Croquetes enjoyer (talk) 13:15, 20 November 2023 (UTC)[reply]

Talk:Markov chains on a measurable state space

Merger with Harris chain

Addition of non-time-homogeneous case

Navigation menu

Search