Comments on a problem of Chernoff and Petkau
A new method is used to study the optimal stopping set corrected for discreteness introduced by \textit{H. Chernoff} [Ann. Math. Statistics 36, 55-68 (1965; Zbl 0246.62084)] and studied by \textit{H. Chernoff} and \textit{A. J. Petkau} [Ann. Probab. 4, 875-889 (1976; Zbl 0347.62064)]. The discrete boundary is asymptotically the optimal boundary for a Wiener process translated downward by a constant amount. This amount is shown to be an ``excess over the boundary'' term, and this method yields it as a simple integral involving the characteristic function of the random walk.
scientific article; zbMATH DE number 4076212