Functional central limit theorems and their associated large deviation principles for products of random matrices

Joseph C. Watkins

doi:10.1007/BF00319982

Functional central limit theorems and their associated large deviation principles for products of random matrices

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Abstract

This paper establishes a functional central limit theorem for a product of random matrices. The sequence of matrices form a stationary process which is a φ-mixing. The individual matrices in the product become closer and closer to the identity matrix with longer and longer products. In addition, these perturbations from the identity matrix have mean zero. A large deviation principle for the limit process is proved.

Original language	English (US)
Pages (from-to)	133-166
Number of pages	34
Journal	Probability Theory and Related Fields
Volume	76
Issue number	2
DOIs	https://doi.org/10.1007/BF00319982
State	Published - Oct 1987
Externally published	Yes

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/BF00319982

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abstract = "This paper establishes a functional central limit theorem for a product of random matrices. The sequence of matrices form a stationary process which is a φ-mixing. The individual matrices in the product become closer and closer to the identity matrix with longer and longer products. In addition, these perturbations from the identity matrix have mean zero. A large deviation principle for the limit process is proved.",

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AB - This paper establishes a functional central limit theorem for a product of random matrices. The sequence of matrices form a stationary process which is a φ-mixing. The individual matrices in the product become closer and closer to the identity matrix with longer and longer products. In addition, these perturbations from the identity matrix have mean zero. A large deviation principle for the limit process is proved.

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Functional central limit theorems and their associated large deviation principles for products of random matrices

Abstract

ASJC Scopus subject areas

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