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Upper bounds on Rubinstein distances on configuration spaces and applications

Abstract : In this paper, we provide upper bounds on several Rubinstein-type distances on the configuration space equipped with the Poisson measure. Our inequalities involve the two well-known gradients, in the sense of Malliavin calculus, which can be defined on this space. Actually, we show that depending on the distance between configurations which is considered, it is one gradient or the other which is the most effective. Some applications to distance estimates between Poisson and other more sophisticated processes are also provided, and an application of our results to tail and isoperimetric estimates completes this work.
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Contributor : Laurent Decreusefond Connect in order to contact the contributor
Submitted on : Monday, March 22, 2010 - 6:18:16 PM
Last modification on : Tuesday, October 25, 2022 - 11:58:10 AM
Long-term archiving on: : Thursday, September 23, 2010 - 12:19:57 PM


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  • HAL Id : hal-00347899, version 2
  • ARXIV : 0812.3221


Laurent Decreusefond, Aldéric Joulin, Nicolas Savy. Upper bounds on Rubinstein distances on configuration spaces and applications. Communications on Stochastic Analysis, 2010, 4 (3), pp.377--399. ⟨hal-00347899v2⟩



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