Timeline for mutual hitting measure between two sets
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2011 at 1:42 | answer | added | James Propp | timeline score: 2 | |
| Feb 18, 2011 at 1:40 | comment | added | James Propp | I added the words "finite" and "irreducible". Thanks, George. George's comments made me realize that my problem has a simple answer: Just create a new Markov chain with one or two states corresponding to each state of the original chain, according to whether the walk's most recent visit to $X_1 \cup X_2$ visited $X_1$ or $X_2$. Then $\mu_1$ and $\mu_2$ are stationary measures for return-maps of this chain. Sorry not to have thought harder before posting... | |
| Feb 18, 2011 at 1:35 | history | edited | James Propp | CC BY-SA 2.5 |
added 9 characters in body
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| Feb 17, 2011 at 22:59 | comment | added | George Lowther | I take it you are looking at finite state space? And irreducible? In which case you can look at the sequence of hitting times $T_1,T_2,\ldots$ of, alternately, $X_1$ and $X_2$. Then, if $M_t$ is your markov chain, $M_{T_k}$ is an irreducible chain on $X_1\cup X_2$ with unique stationary distribution $(\mu_1+\mu_2)/2$. | |
| Feb 17, 2011 at 22:26 | history | asked | James Propp | CC BY-SA 2.5 |