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

Junichi Imai, Reiichiro Kawai

研究成果: Article査読

19 被引用数 (Scopus)

抄録

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 Imai and Kawai [29] and Rosiski (2007) [3], 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.

本文言語English
ページ(範囲)4411-4425
ページ数15
ジャーナルPhysica A: Statistical Mechanics and its Applications
390
23-24
DOI
出版ステータスPublished - 2011 11 1

ASJC Scopus subject areas

  • 統計学および確率
  • 凝縮系物理学

フィンガープリント

「On finite truncation of infinite shot noise series representation of tempered stable laws」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル