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On finite truncation of infinite shot noise series representation of tempered stable laws

By Junichi Imai and Reiichiro Kawai

Abstract

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.2011.07.028Tempered stable processes are widely used in various fields of application as alternatives with finite\ud second moment and long-range Gaussian behaviors to stable processes. Infinite shot noise series representation\ud is the only exact simulation method for the tempered stable process and has recently attracted\ud attention for simulation use with ever improved computational speed. In this paper, we derive series\ud representations for the tempered stable laws of increasing practical interest through the thinning, rejection,\ud and inverse Lévy measure methods. We make a rigorous comparison among those representations,\ud including the existing one due to [18, 34], in terms of the tail mass of Lévy measures which can be\ud simulated under a common finite truncation scheme. The tail mass are derived in closed form for some\ud representations thanks to various structural properties of the tempered stable laws. We prove that the\ud representation via the inverse Lévy measure method achieves a much faster convergence in truncation\ud to the infinite sum than all the other representations. Numerical results are presented to support our\ud theoretical analysis.Peer-reviewedPost-prin

Topics: Infinitely divisible random vector, Inverse Levy measure method, Rejection method, Sample path simulation, Shot noise method, Tempered stable process, Thinning method
Publisher: Elsevier
Year: 2011
DOI identifier: 10.1016/j.physa.2011.07.028
OAI identifier: oai:lra.le.ac.uk:2381/9978
Journal:

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