Journal of the Korean Mathematical Society (대한수학회지)
- Volume 32 Issue 3
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- Pages.427-446
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- 1995
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
An empirical clt for stationary martingale differences
Abstract
Let S be a set and B be a $\sigma$-field on S. We consider $(\Omega = S^Z, T = B^z, P)$ as the basic probability space. We denote by T the left shift on $\Omega$. We assume that P is invariant under T, i.e., $PT^{-1} = P$, and that T is ergodic. We denote by $X = \cdots, X_-1, X_0, X_1, \cdots$ the coordinate maps on $\Omega$. From our assumptions it follows that ${X_i}_{i \in Z}$ is a stationary and ergodic process.
Keywords
- Empirical CLT;
- stationary martingale differences;
- eventual uniform equicontinuity;
- metric entropy with bracketing.