On importance sampling with mixtures for random walks with heavy tails
On importance sampling with mixtures for random walks with heavy tails
复制标题
关于重尾随机游走的混合重要性采样
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Jens Svensson
中科院分区：
文献类型：
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作者：
H. Hult;Jens Svensson
研究了基于混合数据的状态相关重要性抽样算法。算法的目的是计算尾概率的重尾随机游动。假设随机游走的增量具有规则变化的分布。对于相当一般的混合算法，给出了获得有界相对误差的充分条件。两个新的例子，称为广义帕累托混合和缩放混合，介绍。这两个例子有很好的渐近性质，并在现有的一些算法相比，他们是非常容易实现的。数值实验表明，它们的性能。最后证明了这类混合算法可以设计成相对误差为零。
State-dependent importance sampling algorithms based on mixtures are considered. The algorithms are designed to compute tail probabilities of a heavy-tailed random walk. The increments of the random walk are assumed to have a regularly varying distribution. Sufficient conditions for obtaining bounded relative error are presented for rather general mixture algorithms. Two new examples, called the generalized Pareto mixture and the scaling mixture, are introduced. Both examples have good asymptotic properties and, in contrast to some of the existing algorithms, they are very easy to implement. Their performance is illustrated by numerical experiments. Finally, it is proved that mixture algorithms of this kind can be designed to have vanishing relative error.