摘要翻译：
在本文中，我们考虑了一些可以解释为线性滤波器输出的$\sigma$-有限测度。我们假设这些测度具有规则变化的尾巴，并研究线性滤波器的输入是否也具有规则变化的尾巴。这与有限测度中存在的一种特殊的对消性质有关，而这种对消性质又与某些函数方程解的唯一性有关。我们开发的技术应用于I.I.D.的加权和。随机变量，独立随机变量的乘积，以及关于L\'evy运动的随机积分。
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英文标题：
《Inverse problems for regular variation of linear filters, a cancellation
  property for $\sigma$-finite measures and identification of stable laws》
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作者：
Martin Jacobsen, Thomas Mikosch, Jan Rosi\'nski, Gennady Samorodnitsky
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  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 L\'evy motions.
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PDF链接：
https://arxiv.org/pdf/712.0576