Exact simulation of Brownian diffusions with drift admitting jumps
- In this paper, using an algorithm based on the retrospective rejection sampling scheme introduced in [A. Beskos, O. Papaspiliopoulos, and G. O. Roberts,Methodol. Comput. Appl. Probab., 10 (2008), pp. 85-104] and [P. Etore and M. Martinez, ESAIM Probab.Stat., 18 (2014), pp. 686-702], we propose an exact simulation of a Brownian di ff usion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical di ffi culty due to the presence of t w o jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.
| Author details: | David DereudreORCiD, Sara MazzonettoORCiDGND, Sylvie RoellyGND |
|---|---|
| DOI: | https://doi.org/10.1137/16M107699X |
| ISSN: | 1064-8275 |
| ISSN: | 1095-7197 |
| Title of parent work (English): | SIAM journal on scientific computing |
| Publisher: | Society for Industrial and Applied Mathematics |
| Place of publishing: | Philadelphia |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2017/05/09 |
| Publication year: | 2017 |
| Release date: | 2022/11/09 |
| Tag: | Brownian motion with discontinuous drift; exact simulation methods; skew Brownian motion; skew diffusions |
| Volume: | 39 |
| Issue: | 3 |
| Number of pages: | 30 |
| First page: | A711 |
| Last Page: | A740 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
| 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik | |
| Peer review: | Referiert |
| License (German): |  CC-BY - Namensnennung 4.0 International |
