Electronic Communications in Probability

Multivariate Gaussian approximations on Markov chaoses

Simon Campese, Ivan Nourdin, Giovanni Peccati, and Guillaume Poly

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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.

Article information

Electron. Commun. Probab., Volume 21 (2016), paper no. 48, 9 pp.

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

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 60J99: None of the above, but in this section

Markov diffusion generator Fourth Moment Theorem multivariate normal approximations

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Campese, Simon; Nourdin, Ivan; Peccati, Giovanni; Poly, Guillaume. Multivariate Gaussian approximations on Markov chaoses. Electron. Commun. Probab. 21 (2016), paper no. 48, 9 pp. doi:10.1214/16-ECP4615. https://projecteuclid.org/euclid.ecp/1467399737

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