Quenched Central Limit Theorems for Sums of Stationary Processes

TL;DR

This paper investigates conditions under which stationary processes satisfy quenched central limit theorems, demonstrating that certain boundary conditions are insufficient while Hannan's condition ensures quenched convergence.

Contribution

It clarifies the relationship between boundary conditions, Hannan's condition, and quenched CLT for stationary processes, providing new theoretical insights.

Findings

Existence of an L^1 boundary does not imply quenched CLT.

Hannan's condition guarantees quenched convergence.

Provides theoretical criteria for quenched CLT applicability.

Abstract

It is shown that the existence of an L^1 co boundary does not imply the quenched version of the central limit theorem. In another result it is shown that Hannan's condition does imply quenched convergence for an appropriately centered version of the sum.