A variety of phenomena in physical and biological sciences can be mathematically understood by considering the statistical properties of level crossings of random Gaussian processes. Notably, a growing number of these phenomena demand a consideration of correlated level crossings emerging from multiple correlated processes. While many theoretical results have been obtained in the last decades for individual Gaussian level-crossing processes, few results are available for multivariate, jointly correlated threshold crossings. Here, we address bivariate upward crossing processes and derive the corresponding bivariate Central Limit Theorem as well as provide closed-form expressions for their joint level-crossing correlations.

中文翻译：

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多变量平交模型中的互相关和联合高斯性。

通过考虑随机高斯过程的水平交叉的统计特性，可以从数学上理解物理和生物科学中的各种现象。值得注意的是，越来越多的这些现象需要考虑从多个相关过程中出现的相关平交路口。虽然在过去的几十年中已经为单个高斯水平交叉过程获得了许多理论结果，但对于多变量、联合相关的阈值交叉，几乎没有结果可用。在这里，我们解决了双变量向上交叉过程并推导出相应的双变量中心极限定理，并为它们的联合水平交叉相关性提供封闭形式的表达式。