Journal of Scientific Computing

, Volume 79, Issue 3, pp 1477–1504 | Cite as

Exact Simulation of the First-Passage Time of Diffusions

  • S. HerrmannEmail author
  • C. Zucca


Since diffusion processes arise in so many different fields, efficient technics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the first-passage times as a by-product. For efficiency reasons, it is particularly challenging to simulate directly this hitting time by avoiding to construct the whole paths. In the Brownian case, the distribution of the first-passage time is explicitly known and can be easily used for simulation purposes. The authors introduce a new rejection sampling algorithm which permits to perform an exact simulation of the first-passage time for general one-dimensional diffusion processes. The efficiency of the method, which is essentially based on Girsanov’s transformation, is described through theoretical results and numerical examples.


First-passage time Brownian motion Diffusion processes Girsanov’s transformation Exact simulation Randomized algorithm 

2010 AMS Subject Classifications

Primary 65C05 Secondary: 65N75 60G40 



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Authors and Affiliations

  1. 1.Institut de Mathématiques de Bourgogne (IMB) - UMR 5584, CNRSUniversité de Bourgogne Franche-ComtéDijonFrance
  2. 2.Department of Mathematics ‘G. Peano’University of TorinoTurinItaly

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