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Diffusive limits of Lipschitz functionals of Poisson measures

Abstract : Continuous Time Markov Chains, Hawkes processes and many other interesting processes can be described as solution of stochastic differential equations driven by Poisson measures. Previous works, using the Stein's method, give the convergence rate of a sequence of renormalized Poisson measures towards the Brownian motion in several distances, constructed on the model of the Kantorovitch-Rubinstein (or Wasserstein-1) distance. We show that many operations (like time change, convolution) on continuous functions are Lipschitz continuous to extend these quantified convergences to diffuse limits of Markov processes and long-time behavior of Hawkes processes.
Keywords : Stein
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Preprints, Working Papers, ...
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Contributor : Laurent Decreusefond Connect in order to contact the contributor
Submitted on : Monday, July 12, 2021 - 10:57:28 AM
Last modification on : Monday, July 4, 2022 - 9:16:45 AM
Long-term archiving on: : Wednesday, October 13, 2021 - 6:24:17 PM


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  • HAL Id : hal-03283778, version 1


Eustache Besançon, Laure Coutin, Laurent Decreusefond, Pascal Moyal. Diffusive limits of Lipschitz functionals of Poisson measures. 2021. ⟨hal-03283778⟩



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