Level Crossing Probabilities I: One-dimensional Random Walks and Symmetrization
| dc.creator | Siegmund-Schultze, Rainer | |
| dc.creator | von Weizsaecker, Heinrich | |
| dc.date | 2004-06-20 | |
| dc.date | 2006-03-10 | |
| dc.date.accessioned | 2026-07-07T06:36:52Z | |
| dc.date.available | 2026-07-07T06:36:52Z | |
| dc.description | We prove for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n has the order of square root of n. Moment or symmetry assumptions are not necessary. In removing symmetry the (sharp) inequality P(|X+Y| <= 1) < 2 P(|X-Y| <= 1) for independent identically distributed X,Y is used. In part II we shall discuss the connection of this result to 'polygonal recurrence' of higher-dimensional walks and some conjectures on directionally random walks in the sense of Mauldin, Monticino and v.Weizsaecker [5]. | |
| dc.description | 10 pages, some references added, typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0406392 | |
| dc.identifier | http://arxiv.org/abs/math/0406392 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100228 | |
| dc.subject | Probability | |
| dc.subject | 60G51 | |
| dc.title | Level Crossing Probabilities I: One-dimensional Random Walks and Symmetrization | |
| dc.type | text |