论文标题
KAC-RICE公式：主要结果和应用的当代概述
Kac-Rice formula: A contemporary overview of the main results and applications
论文作者
论文摘要
该书开发了著名的矢量价值随机字段的KAC-RICE公式的基本思想。该公式允许计算量度的期望和时刻，以及相对于此量度的积分，这些级别集合了此类领域的一组。在介绍了KAC-RICE公式的历史背景之后，我们给出了共同地区公式的基础演示。该公式取代了多个积分中可变公式的变化，并且该公式的直接应用几乎为kac-rice公式提供了几乎所有级别的公式。我们强调具有所有级别公式的必要性，因为对于某些应用程序，例如，零级的公式。
The book develops the fundamental ideas of the famous Kac-Rice formula for vectorvalued random fields. This formula allows to compute the expectation and moments of the measure, and integrals with respect to this measure, of the sets of levels of such fields. After a presentation of the historical context of the Kac-Rice formula, we give an elementary demonstration of the co-area formula. This formula replaces the change of variable formula in multiple integrals and a direct application of this formula gives the Kac-Rice formula for almost all levels. We emphasize the necessity of having the formula for all levels, because for some applications one needs, for example, the formula for level zero.
