Quenched central limit theorems for a stationary linear process

Dalibor Volny; Michael Woodroofe

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arXiv · 1504.02453

Quenched central limit theorems for a stationary linear process

Dalibor Volny·Michael Woodroofe

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Abstract

We find a sufficient condition under which a central limit theorem for a stationary linear process is quenched. We find a stationary linear process szatisfying the Maxwell-Woodroofe condition for which the variances of partial sums are o(n), there is a CLT with a convergence towards N(0,1) when dividing by standard deviation of the partial sums, and the CLT is not quenched. The weak invariance principle does not hold.

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Dalibor Volny, Michael Woodroofe. 2015-04-09. Quenched central limit theorems for a stationary linear process. https://arxiv.org/abs/1504.02453

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