Timeline for Poincare inequality for the measure of Brownian path
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2015 at 8:24 | comment | added | Martin Hairer | Note also that in the case mentioned by Nate the log-Sobolev inequality holds as well, which gives you quite a bit more than the Poincaré inequality. | |
| May 1, 2015 at 6:46 | comment | added | Nate Eldredge | In this context I think it's more usual to consider the Malliavin derivative (and its Cameron-Martin norm) instead of Frechét. The Poincaré inequality does hold in that case (of course you have to restrict to $f$ with $\int f\,d\mu = 0$). You can find this, and an involved discussion of the many notions of differentiability (which I have not taken the time to unwind) in Chapter 5 of V. Bogachev's book Gaussian Measures. | |
| May 1, 2015 at 6:24 | history | asked | gregarki khayal | CC BY-SA 3.0 |