卷积公式的应用与推广

Application and Generalization of Convolution Formula

摘要: 卷积属于积分运算，也是人为定义的运算，常常出现在广义函数和泛函分析当中，而卷积形式在概率论中就是两个随机变量独立和的密度。本文总结了一些关于卷积的性质和定理，对卷积在概率论方面的应用进行了深入的分析，使得求解概率密度等题型能够快速得出答案，并对卷积公式进行了推广，进一步深化了卷积公式的应用。

Abstract: Convolution is an integral operation, which is also artificially defined and often appears in generalized function and functional analysis, while the convolution form in probability theory is the density of the independent sum of two random variables. In this paper, some properties and theorems of convolution are summarized, and the application of convolution in probability theory is deeply analyzed, so that the solution of probability density and other questions can be quickly answered, and the convolution formula is promoted, further deepening the application of convolution formula.