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Exact simulation of Brownian diffusions with drift admitting jumps

  • Using an algorithm based on a retrospective rejection sampling scheme, we propose an exact simulation of a Brownian diffusion 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 difficulty due to the presence of two jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.

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Metadaten
Author:David Dereudre, Sara Mazzonetto, Sylvie RoellyGND
URN:urn:nbn:de:kobv:517-opus4-91049
ISSN:2193-6943 (online)
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (5 (2016) 7)
Publisher:Universitätsverlag Potsdam
Place of publication:Potsdam
Document Type:Preprint
Language:English
Year of first Publication:2016
Year of Completion:2016
Publishing Institution:Universität Potsdam
Publishing Institution:Universitätsverlag Potsdam
Release Date:2016/05/25
Tag:Brownian motion with discontinuous drift; exact simulation method; skew Brownian motion; skew diffusion
Volume:5
Issue:7
Pagenumber:25
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H35 Computational methods for stochastic equations [See also 65C30]
65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C05 Monte Carlo methods
65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C30 Stochastic differential and integral equations
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section {04 in that areag 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) / 68Uxx Computing methodologies and applications / 68U20 Simulation [See also 65Cxx]
Publication Way:Universitätsverlag Potsdam
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2016
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht