On Schroedinger's equation, 3-dimensional bessel bridges, and passage time problems
| dc.creator | Hernandez-del-Valle, Gerardo | |
| dc.date | 2009-05-12 | |
| dc.date.accessioned | 2026-07-07T13:14:23Z | |
| dc.date.available | 2026-07-07T13:14:23Z | |
| dc.description | We obtain explicit solutions for the density $φ_T$ of the first-time $T$ that a one-dimensional Brownian process $B$ reaches the twice, continuously differentiable moving boundary $f$ and such that $f''(t)\geq 0$ for all $t\in \mathbb{R}^+$. We do so by finding the expected value of some functionals of a 3-dimensional Bessel bridge $\tilde{X}$ and exploiting its relationship with first-passage time problems as pointed out by Kardaras (2007). It turns out that this problem is related to Schrödinger's equation with time-dependent linear potential, see Feng (2001). | |
| dc.identifier | https://arxiv.org/abs/0905.1971 | |
| dc.identifier | http://arxiv.org/abs/0905.1971 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230194 | |
| dc.subject | Probability | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 60J65,45D05,60J60 (Primary); 45G15 (Secondary) | |
| dc.title | On Schroedinger's equation, 3-dimensional bessel bridges, and passage time problems | |
| dc.type | text |