Analytic crossing probabilities for certain barriers by Brownian motion

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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. © Institute of Mathematical Statistics, 2008.

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APA

Kahale, N. (2008). Analytic crossing probabilities for certain barriers by Brownian motion. Annals of Applied Probability, 18(4), 1424–1440. https://doi.org/10.1214/07-AAP488

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