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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 ISSN 0304-4149.

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Official URL: https://doi.org/10.1016/j.spa.2021.09.008

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > 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:
DateEvent
December 2021Published
17 September 2021Available
8 September 2021Accepted
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
Date of first compliant deposit: 22 October 2021
Date of first compliant Open Access: 17 September 2022
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/N51012[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
2018-000009- 01EXTF-00624 CVU699Consejo Nacional de Ciencia y Tecnologíahttp://dx.doi.org/10.13039/501100003141
8049-00021BSapere Aude Starting Granthttps://fundit.fr/en/calls/sapere-aude-dff-starting-grant-denmark

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