论文标题
随机间隔的固定高斯工艺的逗留
Sojourns of Stationary Gaussian Processes over a Random Interval
论文作者
论文摘要
我们研究了sojourn时间$$ \ int_0^t \ mathbb {i}（x（x（t）> u）dt，$$ as $ u \ to \ infty $的尾巴分布的渐近学，其中$ x $是$ x $ $ x $ $ x $ t $是$ x $ noneney neney newenation nonegative tocal的随机随机变量。 $ t $的尾巴分布的重度影响了渐近技术的形式，导致了四种情况：可集成$ t $的情况，这种情况是定期变化的$ t $，$λ= 1 $ = 1 $ and Index $λ\ in（0,1）$，以及$ t $ $ t $的缓慢变化的尾巴分配。通过分析分数Ornstein-Uhlenbeck过程的分析来说明衍生的发现。
We investigate asymptotics of the tail distribution of sojourn time $$ \int_0^T \mathbb{I}(X(t)> u)dt, $$ as $u\to\infty$, where $X$ is a centered stationary Gaussian process and $T$ is an independent of $X$ nonnegative random variable. The heaviness of the tail distribution of $T$ impacts the form of the asymptotics, leading to four scenarios: the case of integrable $T$, the case of regularly varying $T$ with index $λ=1$ and index $λ\in(0,1)$ and the case of slowly varying tail distribution of $T$. The derived findings are illustrated by the analysis of the class of fractional Ornstein-Uhlenbeck processes.
