Analytic crossing probabilities for certain barriers by Brownian motion

Nabil Kahale

doi:10.1214/07-aap488

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arXiv · 0704.2826

Analytic crossing probabilities for certain barriers by Brownian motion

Nabil Kahale

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Abstract

We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class of barriers on $[0,T]$ by proving a Schwartz distribution version of the method of images. Analytic expressions for crossing probabilities and related densities are given for new explicit and semi-explicit barriers.

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Nabil Kahale. 2008-08-28. Analytic crossing probabilities for certain barriers by Brownian motion. https://doi.org/10.1214/07-aap488

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