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- W4290983222 abstract "Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random vector, and of a target random element composed of Gaussian and Poisson random variables. Several consequences are deduced from this result, in particular: (1) new abstract criteria for multidimensional stable convergence on the Poisson space, (2) a class of mixed limit theorems, involving both Poisson and Gaussian limits, (3) criteria for the asymptotic independence of $U$-statistics obeying to Gaussian and Poisson asymptotic regimes. Our results generalize and unify several previous findings in the field. We provide an application to joint sub-graph counting in random geometric graphs." @default.
- W4290983222 created "2022-08-13" @default.
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- W4290983222 date "2012-09-14" @default.
- W4290983222 modified "2023-09-30" @default.
- W4290983222 title "Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering" @default.
- W4290983222 doi "https://doi.org/10.48550/arxiv.1209.3098" @default.
- W4290983222 hasPublicationYear "2012" @default.
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