Electronic Communications in Probability

Multivariate Gaussian approximations on Markov chaoses

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

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1467399737

Digital Object Identifier
doi:10.1214/16-ECP4615

Mathematical Reviews number (MathSciNet)
MR3522594

Zentralblatt MATH identifier
1345.60012

Subjects
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

Keywords
Markov diffusion generator Fourth Moment Theorem multivariate normal approximations

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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References

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