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Multivariate Gaussian approximations on Markov chaoses. (English) Zbl 1345.60012

Summary: We prove a version of the multidimensional fourth moment theorem for chaotic random vectors, in the general context of Markov diffusion 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 the joint convergence of a given sequence of vectors.

MSC:

60F05 Central limit and other weak theorems
60J35 Transition functions, generators and resolvents
60J60 Diffusion processes
60J99 Markov processes
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