Timeline for discrete stochastic process: exponentially correlated Bernoulli?
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| May 23, 2017 at 12:37 | history | edited | CommunityBot |
replaced http://stackoverflow.com/ with https://stackoverflow.com/
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| May 4, 2010 at 15:13 | answer | added | Yvan Velenik | timeline score: 3 | |
| Apr 15, 2010 at 13:04 | vote | accept | Jason S | ||
| Mar 29, 2010 at 15:29 | answer | added | Andrea Carbone | timeline score: 3 | |
| Mar 16, 2010 at 14:05 | comment | added | Jason S | Looks like the OP did in fact mean c |m-n| ^ (-alpha) for m != n. Oh well, this is still an interesting question to me. :-) | |
| Mar 15, 2010 at 21:02 | answer | added | Did | timeline score: 6 | |
| Mar 15, 2010 at 19:15 | comment | added | Jason S | Yes, that was pointed out to me... but I am suspicious + wondering if the OP meant alpha ^ |m-n|. Using the c |m-n| ^ (-alpha) formula, correlation is undefined for m=n. | |
| Mar 15, 2010 at 18:09 | comment | added | Douglas Zare | By the way, the SO problem is not $\alpha^{|m-n|}$, but $c|m-n|^{-\alpha}$. | |
| Mar 15, 2010 at 17:33 | answer | added | Douglas Zare | timeline score: 11 | |
| Mar 15, 2010 at 15:56 | comment | added | Jason S | ...and I had kind of the same hunch (make a continuous-value process, then use a threshold to produce a binary-value output) but don't quite know how to go about characterizing the output process w/r/t correlation, other than an empirical calculation on the computer. | |
| Mar 15, 2010 at 15:20 | comment | added | Jason S | thx for the suggestion... I'm posting this on behalf of someone else (see the link in the 1st sentence) so I do not know the stringency of their requirements. The problem seemed simple enough to state that I felt I could translate into a "proper" problem statement for mathoverflow. | |
| Mar 15, 2010 at 14:59 | comment | added | Alekk | you could try to take a process $x(t)$ like an Ornstein-Uhlenbeck, that has a correlation structure that decreases exponentially, and then define $B_n = 1_{x(n) > \alpha}$ where $\alpha$ is a well-chosen threshold - I have not done the computations, but I have the feeling that the correlation between these Bernoulli random variables also decreases exponentially. Do you really need the correlation to be equal to $\alpha^{|m-n|}$ ? Would an exponentially decreasing correlation be enough for your particular purpose ? | |
| Mar 15, 2010 at 14:20 | history | asked | Jason S | CC BY-SA 2.5 |