Timeline for Feynman–Kac formula for other operators
Current License: CC BY-SA 4.0
8 events
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| Apr 8 at 7:46 | comment | added | Carlo Beenakker | @JochenGlueck -- the high-order generalizations I linked to in my answer (in particular #4) seem to work around this obstruction by introducing a positive probability measure on a complex space of paths. | |
| Apr 8 at 5:21 | comment | added | Jochen Glueck | "higher order Laplacians" For differential operators of order $>2$ one can't have such a formula because the semigroup generated by such an operator is not positivity preserving. | |
| Apr 7 at 21:25 | comment | added | Aidan Backus | I don't know about a Feynman-Kac formula specifically, but the $p$-Laplacian has a nice probabilistic interpretation which generalizes the Laplacian's interpretation as the infinitesimal generator of Brownian motion, see arxiv.org/abs/math/0607761 | |
| Apr 7 at 19:13 | answer | added | Carlo Beenakker | timeline score: 2 | |
| Apr 7 at 18:56 | comment | added | user479223 | For fractional Laplacians it is $\alpha$ stable Levy processes. Also pretty general elliptic operators correspond to diffusions. | |
| Apr 7 at 18:56 | history | edited | LSpice | CC BY-SA 4.0 |
$p-$ -> $p$-, and other tidying
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| Apr 7 at 18:56 | comment | added | LSpice |
TeX note: instead of 1\ if\ ω([0, t]) \subset \Omega $1\ if\ ω([0, t]) \subset \Omega$, use 1\text{ if $\omega([0, t]) \subset \Omega$} $1\text{ if …}$ (although there are differences of opinion about the scope of \text). In fact, there's no need to keep math mode going at all, so $1$ if $\omega([0, t]) \subset \Omega$ is best of all. Also, in $p-$ Laplacians, the - goes out of math mode (it's a hyphen, not a minus). I edited accordingly. You might also like to know about the {cases} environment: \psi = \begin{cases} 1 & \text{if …} \\ 0 & \text{if …} \end{cases}.
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| Apr 7 at 17:54 | history | asked | Emmie | CC BY-SA 4.0 |