Analytic crossing probabilities for certain barriers by Brownian motion
Probability
2008-08-28 v2 Functional Analysis
Statistics Theory
Statistics Theory
Abstract
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class of barriers on 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.
Cite
@article{arxiv.0704.2826,
title = {Analytic crossing probabilities for certain barriers by Brownian motion},
author = {Nabil Kahale},
journal= {arXiv preprint arXiv:0704.2826},
year = {2008}
}