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On the central limit theorem and law of the iterated logarithm for stationary processes with applications to linear processes. (English) Zbl 0834.60026

Summary: Many of the proofs of various central limit theorems and laws of the iterated logarithm for strictly stationary processes are based on approximating martingales. Here we study on this line the functional central limit theorem and law of the iterated logarithm for stationary processes, not necessarily possessing a coboundary decomposition, with applications to stationary linear processes.

MSC:

60F05 Central limit and other weak theorems
60F15 Strong limit theorems
60F17 Functional limit theorems; invariance principles
60G10 Stationary stochastic processes
60G42 Martingales with discrete parameter
28D05 Measure-preserving transformations
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