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Tempering stable processes

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  • Rosinski, Jan
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    Abstract

    A tempered stable Lévy process combines both the [alpha]-stable and Gaussian trends. In a short time frame it is close to an [alpha]-stable process while in a long time frame it approximates a Brownian motion. In this paper we consider a general and robust class of multivariate tempered stable distributions and establish their identifiable parametrization. We prove short and long time behavior of tempered stable Lévy processes and investigate their absolute continuity with respect to the underlying [alpha]-stable processes. We find probabilistic representations of tempered stable processes which specifically show how such processes are obtained by cutting (tempering) jumps of stable processes. These representations exhibit [alpha]-stable and Gaussian tendencies in tempered stable processes and thus give probabilistic intuition for their study. Such representations can also be used for simulation. We also develop the corresponding representations for Ornstein-Uhlenbeck-type processes.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 117 (2007)
    Issue (Month): 6 (June)
    Pages: 677-707

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    Handle: RePEc:eee:spapps:v:117:y:2007:i:6:p:677-707

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    Related research

    Keywords: Tempered stable distributions and processes Stable processes Lévy processes Ornstein-Uhlenbeck-type processes Shot noise representations;

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    Cited by:
    1. Sebastian, Orzeł & Agnieszka, Wyłomańska, 2010. "Calibration of the subdiffusive arithmetic Brownian motion with tempered stable waiting-times," MPRA Paper 28593, University Library of Munich, Germany.
    2. Borak, Szymon & Misiorek, Adam & Weron, Rafal, 2010. "Models for Heavy-tailed Asset Returns," MPRA Paper 25494, University Library of Munich, Germany.

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