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Implementable coupling of Lévy process and Brownian motion
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Fomichov, Vladimir, González Cázares, Jorge and Ivanovs, Jevgenijs (2021) Implementable coupling of Lévy process and Brownian motion. Stochastic Processes and their Applications, 142 . pp. 407-431. doi:10.1016/j.spa.2021.09.008
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Official URL: https://doi.org/10.1016/j.spa.2021.09.008
Abstract
We provide a simple algorithm for construction of Brownian paths approximating those of a Lévy process on a finite time interval. It requires knowledge of the Lévy process trajectory on a chosen regular grid and the law of its endpoint, or the ability to simulate from that. This algorithm is based on reordering of Brownian increments, and it can be applied in a recursive manner. We establish an upper bound on the mean squared maximal distance between the paths and determine a suitable mesh size in various asymptotic regimes. The analysis proceeds by reduction to the comonotonic coupling of increments. Applications to model risk and multilevel Monte Carlo are discussed in detail, and numerical examples are provided.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science > Statistics | ||||||||||||
| SWORD Depositor: | Library Publications Router | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Lévy processes, Brownian motion processes, Approximation algorithms, Monte Carlo method | ||||||||||||
| Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||||||
| Publisher: | Elsevier | ||||||||||||
| ISSN: | 0304-4149 | ||||||||||||
| Official Date: | December 2021 | ||||||||||||
| Dates: |
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| Volume: | 142 | ||||||||||||
| Page Range: | pp. 407-431 | ||||||||||||
| DOI: | 10.1016/j.spa.2021.09.008 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| RIOXX Funder/Project Grant: |
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