Timeline for Functional integral formulas for the wave equation and other hyperbolic PDEs
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| S Sep 3 at 20:11 | history | suggested | user479223 |
Added stochastic calculus tag.
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| Sep 2 at 20:42 | review | Suggested edits | |||
| S Sep 3 at 20:11 | |||||
| Sep 2 at 20:12 | answer | added | user479223 | timeline score: 1 | |
| Sep 2 at 20:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 5 at 19:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 6 at 18:09 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 8, 2023 at 18:33 | comment | added | Denis Serre | You need two initial conditions for the wave equation. I understand that $u(0,x)=f(x)$, but what is $u_t(0,x)$ ? | |
| Sep 8, 2023 at 18:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 9, 2023 at 17:51 | answer | added | Thomas Kojar | timeline score: 0 | |
| Jun 25, 2023 at 3:35 | comment | added | Thomas Kojar | As they mention in cs.fsu.edu/~mascagni/MCPDE_FSU.pdf "I In general MCMs for hyperbolic PDEs (like the wave equation: utt = c 2uxx ) are hard to derive as Brownian motion is fundamentally related to diffusion (parabolic PDEs) and to the equilibrium of diffusion processes (elliptic PDEs), in contrast hyperbolic problems model distortion free information propagation which is fundamentally nonrandom" | |
| Jun 25, 2023 at 3:32 | comment | added | Thomas Kojar | to be clear, it seems unlikely that the wave equation has some Brownian motion representation because in the proof of Feyman-Kac we use the Ito-formula which involves single-time derivative, not double. | |
| Jun 25, 2023 at 3:30 | comment | added | Thomas Kojar | For an alternative approach see the follow up work "Intermittency for the wave and heat equations with fractional noise in time" arxiv.org/abs/1311.0021, where they mention the above functional-path formula. | |
| Jun 23, 2023 at 18:41 | history | asked | Emily | CC BY-SA 4.0 |