Invertibility of functionals of the Poisson process and applications

Abstract

Following previous investigations by {Ü}st{ü}nel [22] about the invertibility of some transformations on the Wiener space, we find some entropic conditions under which a random change of time is invertible on the Poisson space. As a consequence, we provide a new construction of Hawkes processes. We also establish a new variational representation of the entropy.

References in corpus (2)

• Clark--Ocone formula and variational representation for Poisson functionals
• Upper bounds on Rubinstein distances on configuration spaces and applications