Energy image density property and the lent particle method for Poisson measures

TL;DR

This paper presents a novel approach combining energy image density properties and the lent particle method to analyze the absolute continuity of Poisson functionals, offering new tools for stochastic analysis.

Contribution

It introduces the energy image density property and the lent particle method as innovative techniques for studying Poisson measures.

Findings

Establishes conditions for absolute continuity of Poisson functionals

Develops the lent particle method for stochastic analysis

Provides new insights into Dirichlet forms and Poisson measures

Abstract

We introduce a new approach to absolute continuity of laws of Poisson functionals. It is based on the {\it energy image density} property for Dirichlet forms and on what we call {\it the lent particle method} which consists in adding a particle and taking it back after some calculation.