Timeline for when are two Markov chains same distributions
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 14, 2013 at 13:36 | comment | added | Steve Huntsman | mathoverflow.net/questions/14729 | |
| Apr 14, 2013 at 4:51 | comment | added | Yoav Kallus | Under the conditions you list, and with $\pi$ given, I think that $P$ can be described by specifying for each unordered pair $\lbrace i,j\rbrace$ a transition rate $P_{ij}$. The reverse rate $P_{ji}$ is determined by detailed balanced. But for each pair one rate is completely free and independent of all other rates so long as you satisfy ergodicity ($(P^n)_{ij}>0$ for some $n$). | |
| Apr 14, 2013 at 4:18 | comment | added | Sesh | Not sure if much is implied. Consider a finite state space (of size n), and consider the Markov Chain given by random walks on a (non-bipartite) d-regular graph on n vertices. Regardless of the structure of the graph (and the value d), the stationary distribution is uniform. This is a very large set of graphs, and there isn't much structural similarity between these graphs. | |
| Apr 14, 2013 at 3:59 | history | asked | user24367 | CC BY-SA 3.0 |