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First passage times of two-dimensional correlated processes : analytical results for the Wiener process and a numerical method for diffusion processes
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Sacerdote, Laura, Tamborrino, Massimiliano and Zucca, Cristina (2016) First passage times of two-dimensional correlated processes : analytical results for the Wiener process and a numerical method for diffusion processes. Journal of Computational and Applied Mathematics, 296 . pp. 275-292. doi:10.1016/j.cam.2015.09.033
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Official URL: http://dx.doi.org/10.1016/j.cam.2015.09.033
Abstract
Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first crossing component and of the position of the second crossing component before its crossing time. First we show that these densities are solutions of a system of Volterra–Fredholm first kind integral equations. Then we propose a numerical algorithm to solve it and we describe how to use the algorithm to approximate the joint density of the first passage times. The convergence of the method is theoretically proved for bivariate diffusion processes. We derive explicit expressions for these and other quantities of interest in the case of a bivariate Wiener process, correcting previous misprints appearing in the literature. Finally we illustrate the application of the method through a set of examples.
| Item Type: | Journal Article | ||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||
| Divisions: | Faculty of Science > Statistics | ||||||||||
| Library of Congress Subject Headings (LCSH): | Brownian motion processes | ||||||||||
| Journal or Publication Title: | Journal of Computational and Applied Mathematics | ||||||||||
| Publisher: | Elseivier Science BV | ||||||||||
| ISSN: | 0377-0427 | ||||||||||
| Official Date: | April 2016 | ||||||||||
| Dates: |
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| Volume: | 296 | ||||||||||
| Page Range: | pp. 275-292 | ||||||||||
| DOI: | 10.1016/j.cam.2015.09.033 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||
| Funder: | University of Torino |
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