Multivariate Gaussian approximations on Markov chaoses | Zendy

Simon Campese | Zendy; Ivan Nourdin | Zendy; Giovanni Peccati | Zendy; Guillaume Poly | Zendy

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Multivariate Gaussian approximations on Markov chaoses

Author(s) -

Simon Campese,

Ivan Nourdin,

Giovanni Peccati,

Guillaume Poly

Publication year - 2016

Publication title -

electronic communications in probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.236

H-Index - 38

ISSN - 1083-589X

DOI - 10.1214/16-ecp4615

Subject(s) - mathematics , sequence (biology) , moment (physics) , context (archaeology) , convergence (economics) , markov chain , generator (circuit theory) , gaussian , markov process , weak convergence , convergence of random variables , chaotic , approximations of π , multivariate statistics , random variable , statistics , power (physics) , computer science , paleontology , genetics , physics , computer security , classical mechanics , economics , asset (computer security) , biology , economic growth , artificial intelligence , quantum mechanics

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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