Mixing of Poisson random measures under interacting transformations

TL;DR

This paper establishes conditions under which interacting transformations of spatial Poisson point processes exhibit mixing of all orders, extending classical deterministic results using moment and covariance identities.

Contribution

It introduces sufficient conditions for mixing of all orders in Poisson processes under interacting transformations, generalizing previous deterministic transformation results.

Findings

Provides new sufficient conditions for mixing of all orders.

Extends classical deterministic transformation results.

Uses moment and covariance identities for Poisson stochastic integrals.

Abstract

We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical result in the case of deterministic transformations of Poisson measures. The approach relies on moment and covariance identities for Poisson stochastic integrals with random integrands.