Timeline for Question regarding the Wick tensor in white noise analysis
Current License: CC BY-SA 4.0
4 events
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| Dec 3, 2020 at 10:20 | comment | added | Chaos | This may be a matter of notation but is there a proper meaning for $:x^{\otimes n}:$? Is it the same as $x\diamond \cdots \diamond x$? But this doesn't make sense since $x$ is not a random variable, it's actually a tempered distribution. | |
| Dec 3, 2020 at 10:19 | comment | added | Chaos | Hey Martin, I recently came back to this question. Sorry for not giving you any feedback, I've been pretty busy with courses and trying to figure out what my thesis will be about haha. I find your answer quite interesting, but I still feel dubious. In particular regarding the concept of Wick tensor. Namely when I write $\langle :x^{\otimes n}:, f^{\otimes n}\rangle$ I know that this is equivalent to write $I(f)\diamond \cdots \diamond I(f)$, where the stochastic integrals (random variables) are evaluated at the fixed $x$ (chance parameter). | |
| Aug 28, 2020 at 19:30 | history | edited | Martin Hairer | CC BY-SA 4.0 |
Not all formal power series can be multiplied....
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| Aug 28, 2020 at 15:32 | history | answered | Martin Hairer | CC BY-SA 4.0 |