Strong and conditional invariance principles for samples attracted to stable laws
Strong and conditional invariance principles for samples attracted to stable laws
复制标题
受稳定规律吸引的样本的强条件不变性原理
DOI：
10.1007/s004400050110
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发表时间：
1997
影响因子：
2
通讯作者：
M. Ryznar
中科院分区：
文献类型：
--
作者：
R. LePage;K. Podgórski;M. Ryznar
总结。我们证明了I.I.D.序列的归一化部分和过程的一个表示几乎必然收敛。α-稳定律的吸引域中的随机变量，α<；2.利用稳定律的勒佩奇级数表示，我们得到了极限的显式形式。这些结果的一个结果是条件不变性原理，它应用于期权定价以及按符号和排列进行重采样。
Summary. We prove almost sure convergence of a representation of normalized partial sum processes of a sequence of i.i.d. random variables from the domain of attraction of an α-stable law, α<2. We obtain an explicit form of the limit in terms of the LePage series representation of stable laws. One consequence of these results is a conditional invariance principle having applications to option pricing as well as to resampling by signs and permutations.