Open Access
2016 Multivariate Gaussian approximations on Markov chaoses
Simon Campese, Ivan Nourdin, Giovanni Peccati, Guillaume Poly
Electron. Commun. Probab. 21: 1-9 (2016). DOI: 10.1214/16-ECP4615


We prove a version of the multidimensional Fourth Moment Theorem for chaotic random vectors, in the general context of diffusion Markov generators. In addition to the usual componentwise convergence and unlike the infinite-dimensional Ornstein-Uhlenbeck generator case, another moment-type condition is required to imply joint convergence of of a given sequence of vectors.


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Simon Campese. Ivan Nourdin. Giovanni Peccati. Guillaume Poly. "Multivariate Gaussian approximations on Markov chaoses." Electron. Commun. Probab. 21 1 - 9, 2016.


Received: 8 October 2015; Accepted: 16 May 2016; Published: 2016
First available in Project Euclid: 1 July 2016

zbMATH: 1345.60012
MathSciNet: MR3522594
Digital Object Identifier: 10.1214/16-ECP4615

Primary: 60F05 , 60J35 , 60J99

Keywords: Fourth moment theorem , Markov diffusion generator , multivariate normal approximations

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