Timeline for Equivalent Definitions of Gaussian Process?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 15, 2019 at 2:32 | comment | added | jwyao | @NateEldredge Thanks. But I still don't understand why bounded linear operator on Gaussian process is Gaussian. Can you explain more? | |
| Apr 15, 2019 at 2:06 | comment | added | Nate Eldredge | mathoverflow.net/questions/256541/…. | |
| Apr 15, 2019 at 2:04 | comment | added | Nate Eldredge | But if you start with bounded linear functionals, the equivalence is clear. One direction is trivial by taking $d=1$. For the other direction, it's an elementary exercise to show that a finite dimensional random vector is Gaussian iff every linear functional of it is Gaussian (easy with Fourier transforms, for instance); and note that if $f : \mathbb{R}^d \to \mathbb{R}$ is linear then $f \circ A$ is a bounded linear functional on $\mathcal{H}$. | |
| Apr 15, 2019 at 2:01 | comment | added | jwyao | @NateEldredge Any reference on this? And if the operator is bounded and linear, does the equivalence hold? | |
| Apr 15, 2019 at 2:00 | comment | added | Nate Eldredge | A discontinuous (unbounded) linear functional of a Gaussian process need not be Gaussian; indeed, typically it won't even be measurable, so saying it's "Gaussian" has no meaning. | |
| Apr 15, 2019 at 1:34 | history | asked | jwyao | CC BY-SA 4.0 |