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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis


CiteScore 2018: 0.66

SCImago Journal Rank (SJR) 2018: 0.319
Source Normalized Impact per Paper (SNIP) 2018: 0.720

Mathematical Citation Quotient (MCQ) 2018: 0.18

Online
ISSN
1569-3961
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Volume 17, Issue 3

Issues

Exact discrete sampling of finite variation tempered stable Ornstein–Uhlenbeck processes

Reiichiro Kawai / Hiroki Masuda
Published Online: 2011-08-29 | DOI: https://doi.org/10.1515/mcma.2011.012

Abstract

Exact yet simple simulation algorithms are developed for a wide class of Ornstein–Uhlenbeck processes with tempered stable stationary distribution of finite variation with the help of their exact transition probability between consecutive time points. Random elements involved can be divided into independent tempered stable and compound Poisson distributions, each of which can be simulated in the exact sense through acceptance-rejection sampling, respectively, with stable and gamma proposal distributions. We discuss various alternative simulation methods within our algorithms on the basis of acceptance rate in acceptance-rejection sampling for both high- and low-frequency sampling. Numerical results illustrate their advantage relative to the existing approximative simulation method based on infinite shot noise series representation.

Keywords.: Acceptance-rejection sampling; high-frequency sampling; Lévy process; Ornstein–Uhlenbeck process; subordinator; transition probability; tempered stable process

About the article

Received: 2011-01-26

Revised: 2011-08-10

Published Online: 2011-08-29

Published in Print: 2011-09-01


Citation Information: Monte Carlo Methods and Applications, Volume 17, Issue 3, Pages 279–300, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma.2011.012.

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