Error calculus and regularity of Poisson functionals : the lent particle method
Nicolas Bouleau (CIRED, Cermics)
TL;DR
This paper introduces a novel method leveraging Lipschitz functional calculus of local Dirichlet forms to analyze Poisson random measures, enhancing the understanding of their regularity properties.
Contribution
It presents the 'lent particle' method, a new approach for applying Dirichlet form calculus to Poisson functionals, which is a significant advancement in stochastic analysis.
Findings
Developed the 'lent particle' method for Poisson functionals.
Established regularity results for Poisson measures using the new method.
Enhanced the analytical tools available for Poisson process analysis.
Abstract
We propose a new method to apply the Lipschitz functional calculus of local Dirichlet forms to Poisson random measures.
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Taxonomy
TopicsRandom Matrices and Applications · Markov Chains and Monte Carlo Methods · Point processes and geometric inequalities