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The overshoot of a random walk with negative drift

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  • Tang, Qihe

Abstract

Let {Sn,n[greater-or-equal, slanted]0} be a random walk starting from 0 and drifting to -[infinity], and let [tau](x) be the first time when the random walk crosses a given level x[greater-or-equal, slanted]0. Some asymptotics for the tail probability of the overshoot S[tau](x)-x, associated with the event ([tau](x)

Suggested Citation

  • Tang, Qihe, 2007. "The overshoot of a random walk with negative drift," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 158-165, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:2:p:158-165
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    References listed on IDEAS

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    1. Asmussen, Søren & Klüppelberg, Claudia, 1996. "Large deviations results for subexponential tails, with applications to insurance risk," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 103-125, November.
    2. Veraverbeke, N., 1977. "Asymptotic behaviour of Wiener-Hopf factors of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 27-37, February.
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    Cited by:

    1. Wang, Kaiyong & Yang, Yang & Yu, Changjun, 2013. "Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1504-1512.
    2. Tang, Qihe & Wei, Li, 2010. "Asymptotic aspects of the Gerber-Shiu function in the renewal risk model using Wiener-Hopf factorization and convolution equivalence," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 19-31, February.

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