M. Domine, MOMENTS OF THE FIRST-PASSAGE TIME OF A WIENER PROCESS WITH DRIFT BETWEEN 2 ELASTIC BARRIERS, Journal of Applied Probability, 32(4), 1995, pp. 1007-1013
The first-passage problem for the one-dimensional Wiener process with
drift in the presence of elastic boundaries is considered. We use the
Kolmogorov backward equation with corresponding boundary conditions to
derive explicit closed-form expressions for the expected value and th
e variance of the first-passage time. Special cases with pure absorbin
g and/or reflecting barriers arise for a certain choice of a parameter
constellation.