Precise large deviation asymptotics for products of random matrices
| Autor: | Hui Xiao, Ion Grama, Quansheng Liu |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques de Bretagne Atlantique (LMBA), Université de Brest (UBO)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS), Grama, Ion |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Unit sphere [MATH.MATH-PR] Mathematics [math]/Probability [math.PR] Matrix norm Lyapunov exponent 01 natural sciences law.invention Combinatorics 010104 statistics & probability symbols.namesake law FOS: Mathematics 0101 mathematics Mathematics Sequence Applied Mathematics Probability (math.PR) 010102 general mathematics [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Invertible matrix Modeling and Simulation symbols Large deviations theory Rate function Random matrix Mathematics - Probability |
| Zdroj: | Stochastic Processes and their Applications Stochastic Processes and their Applications, Elsevier, 2020, 130, pp.5213-5242 |
| ISSN: | 0304-4149 |
| Popis: | Let ( g n ) n ⩾ 1 be a sequence of independent identically distributed d × d real random matrices with Lyapunov exponent λ . For any starting point x on the unit sphere in R d , we deal with the norm | G n x | , where G n ≔ g n … g 1 . The goal of this paper is to establish precise asymptotics for large deviation probabilities P ( log | G n x | ⩾ n ( q + l ) ) , where q > λ is fixed and l is vanishing as n → ∞ . We study both invertible matrices and positive matrices and give analogous results for the couple ( X n x , log | G n x | ) with target functions, where X n x = G n x ∕ | G n x | . As applications we improve previous results on the large deviation principle for the matrix norm ‖ G n ‖ and obtain a precise local limit theorem with large deviations. |
| Databáze: | OpenAIRE |
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