Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

See all formats and pricing
More options …
Volume 17, Issue 3


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


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.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Michele Leonardo Bianchi, Frank J. Fabozzi, and Svetlozar Rachev
SSRN Electronic Journal, 2014
Michele Leonardo Bianchi, Svetlozar Rachev, and Frank J. Fabozzi
SSRN Electronic Journal, 2013
Hasan Fallahgoul and Gregoire Loeper
Annals of Operations Research, 2019
Sean Carnaffan and Reiichiro Kawai
SIAM Journal on Scientific Computing, 2017, Volume 39, Number 5, Page B886
Sean Carnaffan and Reiichiro Kawai
Journal of Physics A: Mathematical and Theoretical, 2017, Volume 50, Number 24, Page 245001
Reiichiro Kawai
Methodology and Computing in Applied Probability, 2017, Volume 19, Number 1, Page 175
Reiichiro Kawai
SIAM Journal on Scientific Computing, 2015, Volume 37, Number 6, Page A2558
Michael Grabchak
Statistical Inference for Stochastic Processes, 2016, Volume 19, Number 1, Page 29
Michele Leonardo Bianchi and Frank J. Fabozzi
Statistical Methods & Applications, 2014, Volume 23, Number 3, Page 353
Reiichiro Kawai
Journal of Theoretical Probability, 2013, Volume 26, Number 4, Page 932
Junichi Imai and Reiichiro Kawai
Journal of Computational and Applied Mathematics, 2013, Volume 253, Page 264

Comments (0)

Please log in or register to comment.
Log in