Level Crossing Probabilities II: Polygonal Recurrence of Multidimensional Random Walks
| dc.creator | Siegmund-Schultze, Rainer | |
| dc.creator | von Weizsaecker, Heinrich | |
| dc.date | 2004-06-22 | |
| dc.date | 2006-03-10 | |
| dc.date.accessioned | 2026-07-07T06:36:52Z | |
| dc.date.available | 2026-07-07T06:36:52Z | |
| dc.description | In part I (math.PR/0406392) we proved for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n is of the maximal order square root of n. In higher dimensions we call a random walk 'polygonally recurrent' (resp. transient) if a.s. infinitely many (resp. finitely many) of the straight lines between two consecutive sites hit a given bounded set. The above estimate implies that three-dimensional random walks with independent components are polygonally transient. Similarly a directionally reinforced random walk on Z^3 in the sense of Mauldin, Monticino and v.Weizsaecker [1] is transient. On the other hand we construct an example of a transient but polygonally recurrent random walk with independent components on Z^2. | |
| dc.description | 23 pages, errors and typos corrected, references added | |
| dc.identifier | https://arxiv.org/abs/math/0406423 | |
| dc.identifier | http://arxiv.org/abs/math/0406423 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100230 | |
| dc.subject | Probability | |
| dc.subject | 60G51 | |
| dc.title | Level Crossing Probabilities II: Polygonal Recurrence of Multidimensional Random Walks | |
| dc.type | text |