摘要翻译：
如果一个多元平稳时间序列的所有有限维分布都是多元正则变化的，则称它是联合正则变化的。这个性质等价于重标级数的条件分布的弱收敛性，假定在一个固定时刻，重标级数到原点的距离超过一个趋于无穷大的阈值。极限对象称为尾过程，允许分解成独立的径向和角分量。在适当的混合条件下，当时间序列远离原点时，这种尾过程允许对记录时间序列的时间和位置的点过程序列的极限进行简明和明确的描述。将该理论应用于具有随机系数矩阵的有限阶多元移动平均。
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英文标题：
《Regularly varying multivariate time series》
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作者：
Bojan Basrak, Johan Segers
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最新提交年份：
2007
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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：
  A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional distribution of the rescaled series given that, at a fixed time instant, its distance to the origin exceeds a threshold tending to infinity. The limit object, called the tail process, admits a decomposition in independent radial and angular components. Under an appropriate mixing condition, this tail process allows for a concise and explicit description of the limit of a sequence of point processes recording both the times and the positions of the time series when it is far away from the origin. The theory is applied to multivariate moving averages of finite order with random coefficient matrices.
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PDF链接：
https://arxiv.org/pdf/707.3989