Multivariate stochastic integrals with respect to independently scattered random measures on {\delta}-rings

TL;DR

This paper develops a comprehensive framework for constructing and characterizing vector-valued infinitely divisible independently scattered random measures and their stochastic integrals, providing new tools for multivariate stochastic analysis.

Contribution

It introduces a general construction method for vector-valued random measures and characterizes integrable functions based on their measure's properties, advancing multivariate stochastic integration theory.

Findings

Constructed vector-valued infinitely divisible independently scattered random measures.

Characterized integrable functions in terms of measure characteristics.

Presented a general construction principle for such measures.

Abstract

In this paper we construct general vector-valued infinite-divisible independently scattered random measures with values in $\mathbb{R}^m$ and their corresponding stochastic integrals. Moreover, given such a random measure, the class of all integrable matrix-valued deterministic functions is characterized in terms of certain characteristics of the random measure. In addition a general construction principle is presented.