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Title: On finite truncation of infinite shot noise series representation of tempered stable laws
Authors: Imai, Junichi
Kawai, Reiichiro
First Published: 31-Jul-2011
Publisher: Elsevier
Citation: Physica A: Statistical Mechanics and its Applications, 2011, 390 (23-24), pp. 4411-4425.
Abstract: Tempered stable processes are widely used in various fields of application as alternatives with finite second moment and long-range Gaussian behaviors to stable processes. Infinite shot noise series representation is the only exact simulation method for the tempered stable process and has recently attracted attention for simulation use with ever improved computational speed. In this paper, we derive series representations for the tempered stable laws of increasing practical interest through the thinning, rejection, and inverse Lévy measure methods. We make a rigorous comparison among those representations, including the existing one due to [18, 34], in terms of the tail mass of Lévy measures which can be simulated under a common finite truncation scheme. The tail mass are derived in closed form for some representations thanks to various structural properties of the tempered stable laws. We prove that the representation via the inverse Lévy measure method achieves a much faster convergence in truncation to the infinite sum than all the other representations. Numerical results are presented to support our theoretical analysis.
DOI Link: 10.1016/j.physa.2011.07.028
ISSN: 0378-4371
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © Elsevier B.V. All rights reserved.
Description: This is the author’s version of a work that was accepted for publication in Physica A: Statistical Mechanics and its Applications. Changes resulting from the publishing process, such as editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica A, 390 (23-24), 2011, pp. 4411-4425. DOI: 10.1016/j.physa.2011.07.028
Appears in Collections:Published Articles, Dept. of Mathematics

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