Integration by parts on the law of the reflecting Brownian motion
| dc.creator | Zambotti, Lorenzo | |
| dc.date | 2004-04-27 | |
| dc.date.accessioned | 2026-07-07T05:07:45Z | |
| dc.date.available | 2026-07-07T05:07:45Z | |
| dc.description | We prove an integration by parts formula on the law of the reflecting Brownian motion $X:=|B|$ in the positive half line, where $B$ is a standard Brownian motion. In other terms, we consider a perturbation of $X$ of the form $X^ε= X+εh$ with $h$ smooth deterministic function and $ε>0$ and we differentiate the law of $X^ε$ at $ε=0$. This infinitesimal perturbation changes drastically the set of zeros of $X$ for any $ε>0$. As a consequence, the formula we obtain contains an infinite dimensional generalized functional in the sense of Schwartz, defined in terms of Hida's renormalization of the squared derivative of $B$ and in terms of the local time of $X$ at 0. We also compute the divergence on the Wiener space of a class of vector fields not taking values in the Cameron-Martin space. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404489 | |
| dc.identifier | http://arxiv.org/abs/math/0404489 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70986 | |
| dc.subject | Probability | |
| dc.subject | 60H07, 60J65, 60H40 | |
| dc.title | Integration by parts on the law of the reflecting Brownian motion | |
| dc.type | text |