Quenched central limit theorems for a stationary linear process

2015/04/09 by Dalibor Volny, Volny, Dalibor, Michael Woodroofe +1
Mathematics · #28D05 #60F05 #60G10 #60G42 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:28D05 #msc:60F05 #msc:60G10 #msc:60G42

paper · pdf · doi:10.48550/arxiv.1504.02453

arxiv created 2015/05/21 · arxiv updated 2015/05/22

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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