The Wiener process between a reflecting and an absorbing barrier

The paper considers a Wiener process between a reflecting and an absorbing barrier and derive a series solution for the transition density of the process and for the density of the time to absorption. If the drift is towards the reflecting barrier, the variance is not too large, and the distance of the barriers is not too small, the leading term of the series derives from imaginary solutions of the basic eigenvalue equation of this problem. It is shown that these leading terms often make the dominant contribution to the complete series. Finally, the paper considers previous attempts by Furth, Cox and Miller, and áto the complete series. Finally, the paper considers previous attempts by F