arXiv:1504.02453 Abstract | arXiv Analytics

arXiv:1504.02453 [math.PR]Abstract References Reviews Resources

Quenched central limit theorems for a stationary linear process

Published 2015-04-09Version 1

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.

Categories: math.PR

Subjects: 60F05, 60G10, 60G42, 28D05

Keywords: quenched central limit theorems, partial sums, weak invariance principle, sufficient condition, stationary linear process szatisfying

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