On integral transformations with a stochastic kernel

Abstract

The aim of this paper is to study the properties of integral transformations of the form ϕ (χ) = ʃ r(y) K(x, y) dy, performed on the function r (y) by means of the stochastic kernel K(x, y). According to the generally accepted terminology, the kernel is called stochastic if it satisfies the conditions (see the article). The study of the properties of the transformed function ϕ (χ) naturally splits into two cases: symmetric and asymmetric F(x, y). The article considers questions about the functional moments of symmetric correlation and about the functional moments of asymmetric correlation.