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Strong invariance principles for dependent random variables. (English) Zbl 1166.60307

Summary: We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions.

MSC:

60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
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