TY - JOUR
T1 - Almost sure relative stability of the overshoot of power law boundaries
AU - Doney, R. A.
AU - Maller, R. A.
PY - 2007/3
Y1 - 2007/3
N2 - 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.
AB - 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.
KW - Curved boundaries
KW - Overshoot of power-law boundaries
KW - Random walk
UR - http://www.scopus.com/inward/record.url?scp=33847310893&partnerID=8YFLogxK
U2 - 10.1007/s10959-006-0040-3
DO - 10.1007/s10959-006-0040-3
M3 - Article
SN - 0894-9840
VL - 20
SP - 47
EP - 63
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 1
ER -