Almost Sure Relative Stability of the Overshoot of Power Law Boundaries

Doney, R. A. and Maller, R. A. (2006) Almost Sure Relative Stability of the Overshoot of Power Law Boundaries. [MIMS Preprint]

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Abstract

We give necessary and sufficient conditions for the almost sure (a.s.) 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 6= 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 nonzero, or the step length has a finite variance and mean zero.

Item Type: MIMS Preprint
Uncontrolled Keywords: Random walk, curved boundaries, overshoot of power law boundaries
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Dr Peter Neal
Date Deposited: 12 Apr 2006
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/214

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