### Overshoots over curved boundaries

R. A. Doney and P. S. Griffin
Source: Adv. in Appl. Probab. Volume 35, Number 2 (2003), 417-448.

#### Abstract

We consider the asymptotic behaviour of a random walk when it exits from a symmetric region of the form {(x, n) : |x| ≤ rnb} as r → ∞. In order to be sure that this actually occurs, we treat only the case where the power b lies in the interval [0,½), and we further assume a condition that prevents the probability of exiting at either boundary tending to 0. Under these restrictions we establish necessary and sufficient conditions for the pth moment of the overshoot to be O(rq), and for the overshoot to be tight, as r → ∞.

First Page:
Primary Subjects: 60G50
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1051201655
Digital Object Identifier: doi:10.1239/aap/1051201655
Mathematical Reviews number (MathSciNet): MR1970482
Zentralblatt MATH identifier: 02040281

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