A note on a composition of two random integral mappings $\J^\be$ and some examples

TL;DR

This paper demonstrates that composing two specific random integral mappings results in another random integral mapping, expanding the understanding of their structural properties with illustrative examples.

Contribution

It shows that the composition of two random integral mappings $ ext{ extbackslash J}^eta$ is itself a random integral mapping, providing new insights into their algebraic structure.

Findings

Composition of two $ ext{ extbackslash J}^eta$ mappings yields a random integral mapping

Provides examples illustrating the composition property

Enhances understanding of the structure of random integral mappings

Abstract

A method of random integral representation, that is, a method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note we show that a composition of two random integral mappings $\J^\be$ is again a random integral mapping. We illustrate our results on some examples.