Timeline for Weak limit of pushforward measures with finite second moments is also a pushforward measure with finite second moment
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 6 at 3:08 | comment | added | Nate Eldredge | In order to get the limiting measure $\nu$ to have finite second moment, the natural sufficient condition would be for the measures $T_n\# \mu$ to have uniformly bounded second moments. | |
| Feb 6 at 3:07 | comment | added | Nate Eldredge | In particular, if $\mu$ is atpmless then $T_n\# \mu$ can be any probability measure whatsoever. So yeah, assuming the measures are of the form $T_n\# \mu$ is no restriction at all. | |
| Feb 6 at 1:05 | review | Close votes | |||
| Feb 20 at 3:05 | |||||
| Feb 6 at 0:44 | comment | added | Christian Remling | The maps $T_n$ aren't really doing anything, you can just focus on the $\nu_n=T_{n*}\mu\to\nu$, and of course $\nu$ need not have finite second moment even if the $\nu_n$'s do. For example, take $\nu=c\sum 1/k^2\delta_k$ and $\nu_n$ as a cut off version of this. | |
| Feb 6 at 0:28 | history | edited | Dongwei | CC BY-SA 4.0 |
added 32 characters in body; edited title
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| Feb 6 at 0:20 | history | asked | Dongwei | CC BY-SA 4.0 |