English

Quenched central limit theorems for a stationary linear process

Probability 2015-05-22 v2

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.

Keywords

Cite

@article{arxiv.1504.02453,
  title  = {Quenched central limit theorems for a stationary linear process},
  author = {Dalibor Volny and Michael Woodroofe},
  journal= {arXiv preprint arXiv:1504.02453},
  year   = {2015}
}
R2 v1 2026-06-22T09:13:47.136Z