Summary
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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Watkins, J.C. Functional central limit theorems and their associated large deviation principles for products of random matrices. Probab. Th. Rel. Fields 76, 133–166 (1987). https://doi.org/10.1007/BF00319982
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DOI: https://doi.org/10.1007/BF00319982
Keywords
- Stochastic Process
- Stationary Process
- Probability Theory
- Identity Matrix
- Limit Theorem