Almost Sure Relative Stability of the Overshoot of Power Law Boundaries |
| |
| Authors: | R. A. Doney R. A. Maller |
| |
| Affiliation: | (1) Department of Mathematics, University of Manchester, Manchester, M60 1QD, UK;(2) School of Finace and Applied Statistics, Australian National University, Canberra, ACT, Australia |
| |
| Abstract: | We give necessary and sufficient conditions for the almost sure relative stability of the overshoot of a random walk when it exits from a two-sided symmetric region with curved boundaries. The boundaries are of power-law type, ±rn b , r > 0, n = 1, 2,..., where 0 ≤ b < 1, b≠ 1/2. In these cases, the a.s. stability occurs if and only if the mean step length of the random walk is finite and non-zero, or the step length has a finite variance and mean zero. |
| |
| Keywords: | Random walk Curved boundaries Overshoot of power-law boundaries |
| 本文献已被 SpringerLink 等数据库收录！ |
|
