### 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 | |

State | Published - Oct 1987 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistics and Probability
- Analysis
- Mathematics(all)

### Cite this

**Functional central limit theorems and their associated large deviation principles for products of random matrices.** / Watkins, Joseph C.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Functional central limit theorems and their associated large deviation principles for products of random matrices

AU - Watkins, Joseph C

PY - 1987/10

Y1 - 1987/10

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=34250107770&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250107770&partnerID=8YFLogxK

U2 - 10.1007/BF00319982

DO - 10.1007/BF00319982

M3 - Article

VL - 76

SP - 133

EP - 166

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 2

ER -