On Durbin's series for the density of first passage times

Journal Article

Durbin (1992) derived a convergent series for the density of the first passage time of a Weiner process to a curved boundary. We show that the successive partial sums of this series can be expressed as the iterates of the standard substitution method for solving an integral equation. The calculation is thus simpler than it first appears. We also show that, under a certain condition, the series converges uniformly. This strengthens Durbin's result of pointwise convergence. Finally, we present a modified procedure, based on scaling, which sometimes works better. These approaches cover some cases that Durbin did not. © Applied Probability Trust 2011.

Full Text

Duke Authors

Cited Authors

  • Zipkin, P

Published Date

  • 2011

Published In

Volume / Issue

  • 48 / 3

Start / End Page

  • 713 - 722

International Standard Serial Number (ISSN)

  • 0021-9002

Digital Object Identifier (DOI)

  • 10.1239/jap/1316796909