Recent advances in invariance principles for stationary sequences

By F. Merlevède, Magda Peligrad, Sergey Utev. 2006

155 citations recorded by the source corpus.

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.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3cf6627f97db52f2a53f36724b3cf96da9937f19

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In Mathematical Physics

Citations in the corpus

Weak convergence of the tail empirical process for dependent sequences (2009, unknown): “[18, 10,11,30] and the references therein.”
Law of the iterated logarithm for stationary processes (2006, background): “Our condition (5) can be checked when a mixing rate is available for a ρ-mixing process; see [12], pages 4–5 for a definition.”
Inequalities and limit theorems for weakly dependent sequences (2013, methodology): “We refer to the books of Meyer (1990) and Devore and Lorentz (1993) for more about these spaces and their properties.”
Convergence to Lévy stable processes under some weak dependence conditions (2009, background): “1), a substantial amount of work has been devoted to extend the central limit theorem and the Donsker’s invariance principle to weakly dependent random variables; see the recent review by Merlevède, Peligrad, and Utev [31] for sequences of random variables with finite variances and Bradley [7], Shao”