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Invariance Principles and Gaussian Approximation for Strictly Stationary Processes

Dalibor Volný
Transactions of the American Mathematical Society
Vol. 351, No. 8 (Aug., 1999), pp. 3351-3371
Stable URL: http://www.jstor.org/stable/118024
Page Count: 21
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Invariance Principles and Gaussian Approximation for Strictly Stationary Processes
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Abstract

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

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