Timeline for Correlation for a discrete time markov chain
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2016 at 9:10 | vote | accept | HolyMonk | ||
| Dec 23, 2016 at 1:03 | answer | added | Nawaf Bou-Rabee | timeline score: 1 | |
| Dec 22, 2016 at 19:50 | comment | added | HolyMonk | Okay great advice. I'll try to do that tomorrow. I'll keep you posted! | |
| Dec 22, 2016 at 19:48 | comment | added | Nate Eldredge | I think if you play around with $|S|=3$ for a while you'll be able to find two chains with the same value for $\ell_1$ but different values for $\ell_2$. | |
| Dec 22, 2016 at 19:37 | comment | added | HolyMonk | Okay I reconsidered it but yes this "one family of functions $f_m$" is the thing I was hoping for that it would exist. The two dimensional case seemed to hint its existence in my eyes but I don't have any justification for this. | |
| Dec 22, 2016 at 19:28 | comment | added | HolyMonk | I will reconsider my question. | |
| Dec 22, 2016 at 19:28 | comment | added | HolyMonk | Yes you make a very valid point. | |
| Dec 22, 2016 at 19:25 | comment | added | Nate Eldredge | I guess I'm also a little confused by the question. It certainly can't be true that there is a single family of functions $f_m$ that does the job for every possible Markov chain, or even for every possible Markov chain on a given fixed state space $S$. And if you allow the family $f_m$ to depend on the chain, then it is trivially true since you just set $f_m(\ell_1)$ to be whatever $\ell_m$ is for that chain. | |
| Dec 22, 2016 at 19:18 | comment | added | HolyMonk | You may assume $S \subseteq \mathbb{R}$ | |
| Dec 22, 2016 at 19:17 | comment | added | Nate Eldredge | I know how correlation of real-valued random variables is defined, but how do you define the correlation of random variables taking values in an abstract set $S$? | |
| Dec 22, 2016 at 15:24 | history | asked | HolyMonk | CC BY-SA 3.0 |