A bound on the expected overshoot for some concave boundaries |
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| Authors: | Albrecht Irle Vladimir Ivanovich Lotov |
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| Affiliation: | 1. University of Kiel, Ludewig-Meyn-Stra?e 4, D-24098, Kiel, Germany
2. Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia
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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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