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

Article type: Research Article

Authors: Nualart, David | Zheng, Guangqu^{; *}

Affiliations: Mathematics Department, University of Kansas, Snow Hall, 1460 Jayhawk blvd, Lawrence, KS 66045-7594, United States. E-mails: nualart@ku.edu, zhengguangqu@gmail.com

Correspondence: [*] Corresponding author. E-mail: zhengguangqu@gmail.com.

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.

Keywords: Oscillatory integral, Breuer–Major theorem, Malliavin calculus, random homogenization

DOI: 10.3233/ASY-191575

Journal: Asymptotic Analysis, vol. 119, no. 3-4, pp. 281-300, 2020