Chaos representations for Marked Point Processes

TL;DR

This paper demonstrates that for many marked point processes, a specially constructed random measure allows for representing all square integrable random variables through iterated integrals, facilitating analysis and computation.

Contribution

It introduces a novel chaos representation framework for marked point processes using a predictable random measure, expanding the tools for stochastic analysis.

Findings

Existence of a random measure with predictable representation property

Iterated integrals span the space of square integrable random variables

Framework applicable to a large class of marked point processes

Abstract

We show that for a large class of marked point processes there exists a random measure m with the predictable representation property such that iterated integrals with respect to m span the space of square integrable random variables.