Distribution of the time of first arrival of a Wiener process at a given boundary

An exact expression is derived for the characteristic function of the distribution of the first arrival time of a Wiener process at a given boundary, which is fixed in time. An approximate expression is obtained for the same characteristic function assuming that the given boundary is a function of time. The properties of the distribution of the first arrival time are analyzed.Translated from Statisticheskie Metody, pp. 31–42, 1980.