<p>I'm trying to find out what is known about time-inhomogeneous ergodic Markov Chains where the transition matrix can vary over time. 
All textbooks and lecture notes I could find initially introduce Markov chains this way but then quickly restrict themselves to the time-homogeneous case where you have one transition matrix. </p>

<p>Obviously, in general such Markov chains might not converge to a unique stationary distribution, but I would be surprised if there isn't a large (sub)class of these chains where convergence is guaranteed. I'm particularly interested in theorems on the mixing time and convergence theorems that state when there exists a stationary distribution.</p>

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2014-05-27T11:16:49.263Z
Isn't there a stationary convergence iff the transition matrix converge?
R B
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2014-05-28T02:23:03.453Z
Well, I was wondering whether this is true but couldn't find a reference.
markov-imitator
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2014-05-28T07:37:44.273Z
I'll try to post this on mathoverlow...
markov-imitator
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2014-05-28T13:26:30.277Z
Cross-posted to http://mathoverflow.net/questions/168398/ .  Next time, if you cross-post, please add links to the questions both ways.
Zsbán Ambrus
<reference-request><co.combinatorics><pr.probability><markov-chains>
Time-inhomogeneous Markov Chains
markov-imitator
# Time-inhomogeneous Markov Chains

(Asked by: username_0 on 2014-05-27)

I'm trying to find out what is known about time-inhomogeneous ergodic Markov Chains where the transition matrix can vary over time.
All textbooks and lecture notes I could find initially introduce Markov chains this way but then quickly restrict themselves to the time-homogeneous case where you have one transition matrix.

Obviously, in general such Markov chains might not converge to a unique stationary distribution, but I would be surprised if there isn't a large (sub)class of these chains where convergence is guaranteed. I'm particularly interested in theorems on the mixing time and convergence theorems that state when there exists a stationary distribution.

**Tags:** reference-request, co.combinatorics, pr.probability, markov-chains

> **Comments:**
> **username_1**: Isn't there a stationary convergence iff the transition matrix converge?  
> **username_0**: Well, I was wondering whether this is true but couldn't find a reference.  
> **username_0**: I'll try to post this on mathoverlow...  
> **username_2**: Cross-posted to http://mathoverflow.net/questions/168398/ .  Next time, if you cross-post, please add links to the questions both ways.  

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## 0 answers

