A quenched invariance principle for stationary processes

Abstract

In this note, we prove a conditionally centered version of the quenched weak invariance principle under the Hannan condition, for stationary processes. In the course, we obtain a (new) construction of the fact that any stationary process may be seen as a functional of a Markov chain.

References in corpus (3)

• Martingale approximations for sums of stationary processes
• On martingale approximations and the quenched weak invariance principle
• Central limit theorem started at a point for additive functionals of reversible Markov chains

Cited by in corpus (10)

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• Invariance principle via orthomartingale approximation
• A compact LIL for martingales in $2$-smooth Banach spaces with applications
• Quenched limit theorems for Fourier transforms and periodogram
• On the quenched CLT for stationary random fields under projective criteria
• Quenched Invariance Principles for the Discrete Fourier Transforms of a Stationary Process
• On the functional CLT for stationary Markov Chains started at a point
• An invariance principle for stationary random fields under Hannan's condition
• A quenched weak invariance principle
• On the Quenched Functional Central Limit Theorem for Stationary Random Fields under Projective Criteria