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