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A bound on the expected overshoot for some concave boundaries

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Abstract

LetX 1,X 2,… be i.i.d. with finite meanμ>0,S n =X 1+…+X n . Forf(n)=n β,c>0 we consider the stopping timesT c =inf{n:S n >c+f(n)} with overshootR c =S T c −(c+f(T c )). For 0<β<1 we give a bound for sup c≥0 ER c in the spirit of Lorden’s well-known inequality forf=0.

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Authors and Affiliations

  1. University of Kiel, Ludewig-Meyn-Straße 4, D-24098, Kiel, Germany

    Albrecht Irle

  2. Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia

    Vladimir Ivanovich Lotov

Authors
  1. Albrecht Irle
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  2. Vladimir Ivanovich Lotov
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Irle, A., Lotov, V.I. A bound on the expected overshoot for some concave boundaries. Metrika 46, 253–267 (1997). https://doi.org/10.1007/BF02717178

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  • DOI: https://doi.org/10.1007/BF02717178

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