Timeline for Information theory for uncountably infinite-dimensional continuous random variable
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2020 at 17:02 | vote | accept | mw19930312 | ||
| Jul 17, 2020 at 20:48 | comment | added | leo monsaingeon | 1) is not an easy task in whole generality, but for example when $R$ is the (law of) a Brownian motion then the RN density can be computed using Girsanov theory, as I mentioned. 2) not really, at least not a canonical one. Again, the Wiener measure is a reasonable choice, but I guess it depends on the applications you have in mind. 3) same as 2), I guess it depends on your applications, but perhpas check out Sanov's theorem for a starting point? | |
| Jul 17, 2020 at 20:37 | history | edited | leo monsaingeon | CC BY-SA 4.0 |
added 8 characters in body
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| Jul 15, 2020 at 17:51 | comment | added | mw19930312 | Hi Leo, thanks for the answer here! While I'm digesting the references, I have some quick questions here. 1) Do we have any convenient way to compute $H(P|R)$? As far as I have concerned, the Radon-Nykodim density is not easy to compute... 2) Is there a good choice of $P$ in infinite-dimensional case? I know that a uniform distribution doesn't exist in infinite-dimensional case... 3) If I want to extend this notion of relative entropy to a space of random variables (e.g., I would like to choose an r.v. under some probability distribution), then what reference measure would be available? | |
| Jul 15, 2020 at 5:47 | history | answered | leo monsaingeon | CC BY-SA 4.0 |