For a zero-mean, unit-variance stationary univariate Gaussian process we derive the probability that a record at the time n, say $X_n$ , takes place, and derive its distribution function. We study the joint distribution of the arrival time process of records and the distribution of the increments between records. We compute the expected number of records. We also consider two consecutive and non-consecutive records, one at time j and one at time n, and we derive the probability that the joint records $(X_j,X_n)$ occur, as well as their distribution function. The probability that the records $X_n$ and $(X_j,X_n)$ take place and the arrival time of the nth record are independent of the marginal distribution function, provided that it is continuous. These results actually hold for a strictly stationary process with Gaussian copulas.

中文翻译：

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时间相关的平稳高斯序列的记录

对于零均值、单位方差的平稳单变量高斯过程，我们推导出当时记录的概率n， 说$X_n$，发生，并导出其分布函数。我们研究了记录到达时间过程的联合分布和记录间增量的分布。我们计算预期的记录数。我们还考虑两个连续的和非连续的记录，一次一个j有时一个n，我们推导出联合记录的概率$(X_j,X_n)$发生，以及它们的分布函数。记录的概率$X_n$和$(X_j,X_n)$发生地点和到达时间n如果它是连续的，则该记录与边际分布函数无关。这些结果实际上适用于具有高斯 copula 的严格平稳过程。