Abstract
We continue the study of the asymptotic behaviour a random walk when it exits from a symmetric region of the form {(x,n): x ≤ rnb} as r → ∞, which was begun in Part I of this work. In contrast to that paper, we are interested in the case where the probability of exiting at the upper boundary tends to 1. In this scenario we treat the case where the power b lies in the interval [0, 1], and we establish necessary and sufficient conditions for the overshoot to be relatively stable in probability (except for the case b = 1/2), and for the pth moment of the overshoot to be 0 (rq) as r → ∞.
Original language | English (US) |
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Pages (from-to) | 1148-1174 |
Number of pages | 27 |
Journal | Advances in Applied Probability |
Volume | 36 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2004 |
Keywords
- Exit time
- Moment of overshoot
- Power-law boundary
- Random walk
- Relative stability
ASJC Scopus subject areas
- Statistics and Probability
- Applied Mathematics