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 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.
| Original language | English |
|---|---|
| Pages (from-to) | 4411-4425 |
| Number of pages | 15 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 390 |
| Issue number | 23-24 |
| DOIs | |
| Publication status | Published - 2011 Nov 1 |
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Keywords
- Infinitely divisible random vector
- Inverse Lévy measure method
- Rejection method
- Sample path simulation
- Shot noise method
- Tempered stable process
- Thinning method
ASJC Scopus subject areas
- Condensed Matter Physics
- Statistics and Probability
Cite this
On finite truncation of infinite shot noise series representation of tempered stable laws. / Imai, Junichi; Kawai, Reiichiro.
In: Physica A: Statistical Mechanics and its Applications, Vol. 390, No. 23-24, 01.11.2011, p. 4411-4425.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On finite truncation of infinite shot noise series representation of tempered stable laws
AU - Imai, Junichi
AU - Kawai, Reiichiro
PY - 2011/11/1
Y1 - 2011/11/1
N2 - 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.
AB - 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.
KW - Infinitely divisible random vector
KW - Inverse Lévy measure method
KW - Rejection method
KW - Sample path simulation
KW - Shot noise method
KW - Tempered stable process
KW - Thinning method
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UR - http://www.scopus.com/inward/citedby.url?scp=80052568655&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2011.07.028
DO - 10.1016/j.physa.2011.07.028
M3 - Article
AN - SCOPUS:80052568655
VL - 390
SP - 4411
EP - 4425
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
IS - 23-24
ER -