Strong and conditional invariance principles for samples attracted to stable laws

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• 作者：Raoul LePage ; Krzysztof Podgórski and Micha? Ryznar
• 关键词：Mathematics Subject Classification (1991) ; 60E07 ; 60F17 ; Secondary 60F15 ; 60G50
• 刊名：Probability Theory and Related Fields
• 出版年：1997
• 出版时间：June 1997
• 年：1997
• 卷：108
• 期：2
• 页码：281-298
• 全文大小：221 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Mathematical and Computational Physics
  Quantitative Finance
  Mathematical Biology
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2064

文摘

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.