Multi-dimensional Gaussian fluctuations on the Poisson space
Giovanni Peccati, Cengbo Zheng (Modal'X, PMA)
TL;DR
This paper develops new multi-dimensional central limit theorems for Poisson measures using advanced probabilistic techniques, extending previous results and providing explicit examples involving Ornstein-Uhlenbeck Lévy processes.
Contribution
It introduces novel multi-dimensional Gaussian approximation results on the Poisson space, expanding the scope of prior work with explicit examples and detailed analysis.
Findings
New multi-dimensional CLTs for Poisson measures
Explicit examples with Ornstein-Uhlenbeck Lévy processes
Extension of previous Gaussian approximation results
Abstract
We study multi-dimensional normal approximations on the Poisson space by means of Malliavin calculus, Stein's method and probabilistic interpolations. Our results yield new multi-dimensional central limit theorems for multiple integrals with respect to Poisson measures -- thus significantly extending previous works by Peccati, Sol\'e, Taqqu and Utzet. Several explicit examples (including in particular vectors of linear and non-linear functionals of Ornstein-Uhlenbeck L\'evy processes) are discussed in detail.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and financial applications · Probability and Risk Models