INVERSE PROBLEMS FOR REGULAR VARIATION OF LINEAR FILTERS, A CANCELLATION PROPERTY FOR σ-FINITE MEASURES AND IDENTIFICATION OF STABLE LAWS

• 成果类型: Article
• 署名作者: Jacobsen, Martin; Mikosch, Thomas; Rosinski, Jan; Samorodnitsky, Gennady
• 署名单位: University of Copenhagen; University of Copenhagen; University of Tennessee System; University of Tennessee Knoxville; Cornell University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP540
• 发表日期: 2009
• 页码: 210-242
• 关键词: random-variables; limit theory; THEOREMS

摘要

In this paper, we consider certain sigma-finite measures which can be interpreted as the output of a linear filter. We assume that these measures have regularly varying tails and study whether the input to the linear filter must have regularly varying tails as well. This turns out to be related to the presence of a particular cancellation property in sigma-finite measures, which in turn, is related to the uniqueness of the solution of certain functional equations. The techniques we develop are applied to weighted sums of i.i.d. random variables, to products of independent random variables, and to stochastic integrals with respect to Levy motions.