We use the concept of excursions for the prediction of random variables without any moment existence assumption. To do so, an excursion metric on the space of random variables is defined which appears to be a kind of a weighted $L^1$-distance. Using equivalent forms of this metric and a specific choice of excursion levels, we formulate the prediction problem as a minimization of a certain target functional. Existence and uniqueness of the solution are discussed. An application to the extrapolation of stationary heavy-tailed random functions illustrates the use of the aforementioned theory. Numerical experiments with the prediction of $\alpha$-stable time series and random fields round up the paper.

翻译：我们使用外游概念来预测随机变量,而无需任何时间存在假设。为此,确定了随机变量空间的外游度量值,这似乎是一种加权的1美元-距离。我们使用等量的度量表和特定游览级别选择,将预测问题表述为某一目标功能的最小化。讨论了解决方案的存在和独特性。对固定式重尾随机功能的外推应用说明了上述理论的使用情况。用数值实验预测$\alpha$- sable时间序列和随机圆绕页的字段。