On simulation of tempered stable random variates
On simulation of tempered stable random variates
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DOI：
10.1016/j.cam.2010.12.014
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发表时间：
2010-03
期刊：
影响因子：
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通讯作者：
Ray Kawai;Hiroki Masuda
中科院分区：
文献类型：
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作者：
Ray Kawai;Hiroki Masuda
研究了稳定性指数大于1的回火稳定随机变量的各种模拟方法，特别是在尺度参数很小的情况下，这对应于步长很短的回火稳定Lévy过程的增量。正在考虑的方法是基于接受拒绝采样，高斯近似的一个小的跳跃组件，和无限散粒噪声系列表示。数值结果讨论的优点，局限性和近似误差和所需的计算工作之间的权衡问题。在给定的计算预算下，Baeumer和Meerschaert（2009）[11]的近似接受-拒绝采样技术在非常小的尺度参数的情况下是最有效和最方便的，而且，可以通过少量的额外计算工作来获得任何期望的精度水平。
Various simulation methods for tempered stable random variates with stability index greater than one are investigated with a view towards practical implementation, in particular cases of very small scale parameter, which correspond to increments of a tempered stable Lévy process with a very short stepsize. Methods under consideration are based on acceptance–rejection sampling, a Gaussian approximation of a small jump component, and infinite shot noise series representations. Numerical results are presented to discuss advantages, limitations and trade-off issues between approximation error and required computing effort. With a given computing budget, an approximative acceptance–rejection sampling technique Baeumer and Meerschaert (2009) [11] is both most efficient and handiest in the case of very small scale parameter and moreover, any desired level of accuracy may be attained with a small amount of additional computing effort.