论文标题
连续时间的尾巴过程和尾巴量度定期改变随机过程
The tail process and tail measure of continuous time regularly varying stochastic processes
论文作者
论文摘要
本文的目的是调查最初针对离散时间固定随机过程（时间序列）引入的极值理论的工具，即尾部过程和尾巴措施，在连续的时间随机过程的框架内，在空间$ \ Mathcal {d} $ ofcàdlàg的空间中的路径$ \ j $ j $ \ jathbb y} $ \ mathbb i} $} $} $} $} $ \ r}拓扑。我们证明，这些对象的基本特性得到了保留，并产生了一些较小的（尽管有趣）。我们首先获得结构性结果，这些结果为$ \ Mathcal {d} $的均相移位不变度量提供表示，然后研究$ \ Mathcal {d} $中随机元素的定期变化。我们提供实际条件并研究几个例子，恢复并扩展已知结果。
The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous time stochastic processes with paths in the space $\mathcal{D}$ of càdlàg functions indexed by $\mathbb{R}$, endowed with Skorohod's $J_1$ topology. We prove that the essential properties of these objects are preserved, with some minor (though interesting) differences arising. We first obtain structural results which provide representation for homogeneous shift-invariant measures on $\mathcal{D}$ and then study regular variation of random elements in $\mathcal{D}$. We give practical conditions and study several examples, recovering and extending known results.
