Invariance principles and Gaussian approximation for strictly stationary processes

Volný, Dalibor

doi:10.1090/S0002-9947-99-02401-0

Invariance principles and Gaussian approximation for strictly stationary processes
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Trans. Amer. Math. Soc. 351 (1999), 3351-3371 Request permission

Abstract:

We show that in any aperiodic and ergodic dynamical system there exists a square integrable process $(f\circ T^{i})$ the partial sums of which can be closely approximated by the partial sums of Gaussian i.i.d. random variables. For $(f\circ T^{i})$ both weak and strong invariance principles hold.

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