标题： 任意分布函数和密度的反卷积 显示英文标题

标题： Deconvolution of Arbitrary Distribution Functions and Densities

摘要： 在本文中，我们恢复了受加性测量误差影响的任意随机变量的分布函数（以及可能的密度）。 这个问题也被称为卷积逆问题，在数学中有着悠久的传统。 我们证明，所考虑的模型总能转换为一个具有对称误差变量的模型，其特征函数的值位于单位区间内。 作为结果，目标变量的特征函数被证明是几何级数的极限。 通过对该级数进行截断，建立了相关分布函数（以及密度）的近似。 这些近似的收敛性质在各种设置中进行了详细研究。 显示英文摘要

摘要： In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in mathematics. We show that the model under consideration always can be transformed to a model with a symmetric error variable, whose characteristic function has its values in the unit interval. As a consequence, the characteristic function of the target variable turns out as the limit of a geometric series. By truncation of this series, an approximation for the associated distribution function (and density) is established. The convergence properties of these approximations are examined in detail across diverse setups.