Timeline for Cameron-Martin theorem for non-Gaussian measures
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 7, 2014 at 15:24 | vote | accept | Tom LaGatta | ||
| Feb 7, 2014 at 3:22 | comment | added | Tom LaGatta | @Miguel: I do like the idea of bootstrapping off the classical Cameron-Martin theorem for Gaussians, if they are available. | |
| Feb 7, 2014 at 3:10 | comment | added | Tom LaGatta | Furthermore, there may not be a Gaussian measure corresponding to covariance k. For example, the identity operator on an infinite-dimensional Hilbert space. | |
| Feb 7, 2014 at 1:16 | comment | added | Nate Eldredge | @Miguel: No, for example $\mathbb{P}$ could be a point mass, or supported on two points. | |
| Feb 7, 2014 at 1:14 | answer | added | Nate Eldredge | timeline score: 4 | |
| Feb 6, 2014 at 23:31 | comment | added | Miguel | So you're assuming $\mathbb{P}$ is such that any two linear coordinates on $X$ are random variables of finite vocariance given by $k$. Does that not imply that $\mathbb{P}$ is absolutely continuous with respect to the Gaussian measure with covariance $k$? | |
| Feb 6, 2014 at 23:09 | history | asked | Tom LaGatta | CC BY-SA 3.0 |