Timeline for What is known about the Gaussian measure of the unit ball in a Hilbert Space?
Current License: CC BY-SA 2.5
5 events
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| Aug 23, 2010 at 1:16 | comment | added | Richard Borcherds | Just to confirm: my answer is for the case of THE Gaussian measure, while Peter Shor's answer is for the case of A Gaussian measure. | |
| Aug 22, 2010 at 23:28 | comment | added | Peter Shor | See my answer for the definition of Gaussian measures on Hilbert spaces: one equivalent definition is that any projection onto a finite-dimensional space must be a Gaussian (with some covariance matrix $\Sigma$). | |
| Aug 22, 2010 at 23:00 | comment | added | RadonNikodym | And yet, your reasoning is perfect... :( Are there non equivalent definitions of Gaussian measures on Hilbert Spaces. | |
| Aug 22, 2010 at 22:54 | comment | added | RadonNikodym | Ok, there is something I am missing. Many books define a Gaussian measure on a Hilbert space $H$ to be a measure such that the push forward measure of every linear functional on $H$ is Gaussian on $\mathbb{R}$. One can then define the mean and covariance of the measure from the mean and variance of these real-valued distributions. So this isn't a Gaussian measure in some sense? | |
| Aug 22, 2010 at 22:08 | history | answered | Richard Borcherds | CC BY-SA 2.5 |