Asymptotic expansions for infinite weighted convolutions of rapidly varying subexponential distributions

• 成果类型: Article
• 署名作者: Barbe, Ph.; McCormick, W. P.
• 署名单位: University System of Georgia; University of Georgia; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0082-1
• 发表日期: 2008
• 页码: 155-180
• 关键词: random-variables; extremes; returns; tails; sums; time

摘要

We establish some asymptotic expansions for infinite weighted convolutions of distributions having rapidly varying subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs to have a general way to calculate higher order expansions, due to possible cancellations of terms. An algebraic methodology is employed to obtain the results.