The first-passage time of the Brownian motion to a curved boundary: an algorithmic approach

Samuel Herrmann 1, * Etienne Tanré 2
* Corresponding author
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases. Several mathematical studies proposed to approximate the pdf in a quite general framework or even to simulate this hitting time using a discrete time approximation of the Brownian motion. The authors study a new algorithm which permits to simulate the first-passage time using an iterating procedure. The convergence rate presented in this paper suggests that the method is very efficient.
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Journal articles
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https://hal.inria.fr/hal-01110387
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Submitted on : Wednesday, January 28, 2015 - 10:07:19 AM
Last modification on : Thursday, February 7, 2019 - 2:28:08 PM

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Samuel Herrmann, Etienne Tanré. The first-passage time of the Brownian motion to a curved boundary: an algorithmic approach. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2016, 38 (1), pp.A196-A215. ⟨10.1137/151006172⟩. ⟨hal-01110387⟩

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