A complete characterization of local martingales which are functions of Brownian motion and its maximum
| dc.creator | Obloj, Jan | |
| dc.date | 2005-04-22 | |
| dc.date.accessioned | 2026-07-07T05:19:21Z | |
| dc.date.available | 2026-07-07T05:19:21Z | |
| dc.description | We prove the max-martingale conjecture given in recent article with Marc Yor. We show that for a continuous local martingale $(N\_t:t\ge 0)$ and a function $H:R x R\_+\to R$, $H(N\_t,\sup\_{s\leq t}N\_s)$ is a local martingale if and only if there exists a locally integrable function $f$ such that $H(x,y)=\int\_0^y f(s)ds-f(y)(x-y)+H(0,0)$. This implies readily, via Levy's equivalence theorem, an analogous result with the maximum process replaced by the local time at 0. | |
| dc.identifier | https://arxiv.org/abs/math/0504462 | |
| dc.identifier | http://arxiv.org/abs/math/0504462 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74991 | |
| dc.subject | Probability | |
| dc.subject | MSC2000: 60G44 | |
| dc.title | A complete characterization of local martingales which are functions of Brownian motion and its maximum | |
| dc.type | text |