Approximations of boundary crossing probabilities for a Brownian motion

Alex Novikov*, Volf Frishling, Nino Kordzakhia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Citations (Scopus)


Using the Girsanov transformation we derive estimates for the accuracy of piecewise approximations for one-sided and two-sided boundary crossing probabilities. We demonstrate that piecewise linear approximations can be calculated using repeated numerical integration. As an illustrative example we consider the case of one-sided and two-sided square-root boundaries for which we also present analytical representations in a form of infinite power series.

Original languageEnglish
Pages (from-to)1019-1030
Number of pages12
JournalJournal of Applied Probability
Issue number4
Publication statusPublished - Dec 1999
Externally publishedYes


  • First passage times
  • Girsanov transformation
  • Numerical integration
  • Werner process


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