Recent advances in invariance principles for stationary sequences

Details Recent advances in invariance principles for stationary sequences Recent advances in invariance principles for stationary sequences

2006-01-13

arxiv.org/abs/math/0601315v2

Probability Surveys 2006, Vol. 3, No. 0, 1-36

Mathematics

Probability

Published at http://dx.doi.org/10.1214/154957806100000202 in the Probability Surveys (http://www.i-journals.org/ps/) by the In

Scientific paper

10.1214/154957806100000202

In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance principles, and also they have interest in themselves. The classes of dependent random variables considered will be martingale-like sequences, mixing sequences, linear processes, additive functionals of ergodic Markov chains.

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