论文标题
在零件公式的多元集成版本中
On a version of a multivariate integration by parts formula for Lebesgue integrals
论文作者
论文摘要
按零件公式进行的多维集成适用于标准假设，即其中一个函数是连续的，而另一个功能是有限的hardy-krause变化。本文在价格和风险范围的概率环境中的最近开发的结果，本文提供了零件公式的集成版本，用于Lebesgue诱导措施诱导功能不可或缺的功能，这些功能可能是不连续的，并且可能具有无限的强硬量变化。为此，我们给出了诱导度量函数的一般定义，并建立了它们的各种属性，例如以三角洲 - 单酮函数来表征。由于按零件公式进行集成，提供了几个收敛结果，从而扩展了Lebesgue诱导函数的积分，以与连续半孔相对于连续的半孔子进行整合的情况。后一类聚合功能包括准孔子，这些函数是许多应用中依赖性结构的界限。
Multidimensional integration by parts formulas apply under the standard assumption that one of the functions is continuous and the other has bounded Hardy-Krause variation. Motivated by recently developed results in the probabilistic context of price and risk bounds, this paper provides a version of an integration by parts formula for the Lebesgue integral of measure-inducing functions which may both be discontinuous and may have infinite Hardy-Krause variation. To this end, we give a general definition of measure-inducing functions and establish various of their properties, such as a characterization in terms of Delta-monotone functions. As a consequence of the integration by parts formula, several convergence results are provided, allowing an extension of the Lebesgue integral of a measure-inducing function to the case where one integrates with respect to a continuous semi-copula. The latter class of aggregation functions includes quasi-copulas which serve as bounds for the dependence structure in many applications.
