Oscillatory Breuer-Major theorem with application to the random corrector problem

Abstract

In this paper, we present an oscillatory version of the celebrated Breuer-Major theorem that is motivated by the random corrector problem. As an application, we are able to prove new results concerning the Gaussian fluctuation of the random corrector. We also provide a variant of this theorem involving homogeneous measures.

arXiv commentV2: Minor revision; to appear in Asymptotic analysis

References in corpus (4)

• Central limit theorems for sequences of multiple stochastic integrals
• Renormalized self-intersection local time for fractional Brownian motion
• Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization
• Polar decomposition of scale-homogeneous measures with application to Lévy measures of strictly stable laws

Cited by in corpus (3)

• Averaging 2d stochastic wave equation
• Averaging Gaussian functionals
• Limit theorems for $p$-domain functionals of stationary Gaussian fields