The overshoot of a random walk with negative drift
نویسنده
چکیده
Let fSn; nX0g be a random walk starting from 0 and drifting to 1, and let tðxÞ be the first time when the random walk crosses a given level xX0. Some asymptotics for the tail probability of the overshoot StðxÞ x, associated with the event ðtðxÞo1Þ, are derived for the cases of heavy-tailed and light-tailed increments. In particular, the formulae obtained fulfill certain uniform requirements. r 2006 Elsevier B.V. All rights reserved.
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