A1 Journal article (refereed)
On first exit times and their means for Brownian bridges (2019)

Geiss, C., Luoto, A., & Salminen, P. (2019). On first exit times and their means for Brownian bridges. Journal of Applied Probability, 56(3), 701-722. https://doi.org/10.1017/jpr.2019.42

JYU authors or editors

Publication details

All authors or editorsGeiss, Christel; Luoto, Antti; Salminen, Paavo

Journal or seriesJournal of Applied Probability



Publication year2019


Issue number3

Pages range701-722

PublisherCambridge University Press; Applied Probability Trust

Publication countryUnited Kingdom

Publication languageEnglish


Publication open accessNot open

Publication channel open access

Web address of parallel published publication (pre-print)https://arxiv.org/abs/1711.06107


For a Brownian bridge from 0 to y, we prove that the mean of the first exit time from the interval (−h, h), h > 0, behaves as O(h2) when h ↓ 0. Similar behaviour is also seen to hold for the three-dimensional Bessel bridge. For the Brownian bridge and threedimensional Bessel bridge, this mean of the first exit time has a puzzling representation in terms of the Kolmogorov distribution. The result regarding the Brownian bridge is applied to provide a detailed proof of an estimate needed by Walsh to determine the convergence of the binomial tree scheme for European options.

Keywordsmathematicsstochastic processesMarkov chains

Free keywordsBessel process; Black-Scholes model; Brownian motion; diffusion process; h-transform; last exit time; Poisson summation formula

Contributing organizations

Ministry reportingYes

Reporting Year2019

JUFO rating1

Last updated on 2024-11-05 at 21:27