Timeline for Gaussian measures on infinite dimensional spaces
Current License: CC BY-SA 4.0
7 events
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| Feb 3, 2021 at 9:56 | comment | added | Chaos | @AbdelmalekAbdesselam Thank you so much for the references! Actually I am more used to work on $S'(\mathbb R)$, this was just a curiosity that I had while reading Da Prato's book. I wanted to know if both approaches were somehow equivalent. Thanks again! | |
| Feb 2, 2021 at 23:56 | comment | added | Abdelmalek Abdesselam | In my first comment I mean Prop 3.4 of arxiv.org/abs/1801.09245 instead. | |
| Feb 2, 2021 at 23:48 | comment | added | Abdelmalek Abdesselam | ...the reference arxiv.org/abs/1502.07335 Finally, if you want an introduction purely with Banach spaces see arxiv.org/abs/1607.03591 | |
| Feb 2, 2021 at 23:47 | comment | added | Abdelmalek Abdesselam | What is your reason for not wanting to work with $S'(\mathbb{R}^n)$? If it is because topological vector spaces scare you look up arxiv.org/abs/1706.09326 You can construct the measure on the bigger space $S'$ and then pick your favorite function space e.g. (weighted) Sobolev or Besov and then prove the measure gives that subspace (Borel set) of $S'$ probability one (for white noise you need the exponent $s$ to be less than $-d/2$). This will give you a measure on that Banach space. See Prop. 3.4 of arxiv.org/abs/1706.09326 Also useful is... | |
| Feb 2, 2021 at 23:32 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
added 1 character in body; edited tags
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| Feb 2, 2021 at 16:07 | history | edited | YCor |
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| Feb 2, 2021 at 14:54 | history | asked | Chaos | CC BY-SA 4.0 |