Talk:Markov chains on a measurable state space

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Merger with Harris chain[edit]

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[edit]

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]