Critical Galton-Watson processes: The maximum of total progenies within a large window
| dc.creator | Fleischmann, Klaus | |
| dc.creator | Vatutin, Vladimir A. | |
| dc.creator | Wachtel, Vitali | |
| dc.date | 2006-01-13 | |
| dc.date.accessioned | 2026-07-07T06:58:53Z | |
| dc.date.available | 2026-07-07T06:58:53Z | |
| dc.description | Consider a critical Galton-Watson process Z={Z_n: n=0,1,...} of index 1+alpha, alpha in (0,1]. Let S_k(j) denote the sum of the Z_n with n in the window [k,...,k+j), and M_m(j) the maximum of the S_k with k moving in [0,m-j]. We describe the asymptotic behavior of the expectation EM_m(j) if the window width j=j_m is such that j/m converges in [0,1] as m tends to infinity. This will be achieved via establishing the asymptotic behavior of the tail probabilities of M_{infinity}(j). | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601333 | |
| dc.identifier | http://arxiv.org/abs/math/0601333 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107542 | |
| dc.subject | Probability | |
| dc.subject | 60J80; 60F17 | |
| dc.title | Critical Galton-Watson processes: The maximum of total progenies within a large window | |
| dc.type | text |