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Infinite Variation Tempered Stable Ornstein-Uhlenbeck Processes with Discrete Observations

By Reiichiro Kawai and Hiroki Masuda


This is an electronic version of an article published in Communications in Statistics - Simulation and Computation, 2012, 41(1), pp. 125-139. Communications in Statistics - Simulation and Computation is available online at: www.tandfonline.comWe investigate transition law between consecutive observations of Ornstein–\ud Uhlenbeck processes of infinite variation with tempered stable stationary\ud distribution. Thanks to the Markov autoregressive structure, the transition law can\ud be written in the exact sense as a convolution of three random components; a\ud compound Poisson distribution and two independent tempered stable distributions,\ud one with stability index in (0, 1) and the other with index in (1, 2). We discuss\ud simulation techniques for those three random elements. With the exact transition law\ud and proposed simulation techniques, sample paths simulation proves significantly\ud more efficient, relative to the known approximative technique based on infinite shot\ud noise series representation of tempered stable Lévy processes.Peer-reviewedPost-prin

Topics: Acceptance-rejection sampling, Lévy process, Ornstein–Uhlenbeck processes, Self decomposability, Tempered stable process, Transition law
Publisher: Taylor & Francis
Year: 2011
DOI identifier: 10.1080/03610918.2011.582561
OAI identifier:

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