Berry–Esseen bounds and moderate deviations for random walks on GLd(R)
| Autor: | Ion Grama, Quansheng Liu, Hui Xiao |
|---|---|
| Přispěvatelé: | Universitat Hildesheim, Institut fur Mathematik and Angewandte Informatik, Hildesheim, Germany, Laboratoire de Mathématiques de Bretagne Atlantique (LMBA), Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Independent and identically distributed random variables September 1 Spectral radius 2021. 2010 Mathematics Subject Classification. Primary 60F10 Applied Mathematics 010102 general mathematics General linear group 16. Peace & justice Random walk 01 natural sciences Exponential function [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010101 applied mathematics Combinatorics 60J05 Modeling and Simulation Projective space Irreducibility 0101 mathematics Secondary 60B20 Operator norm Mathematics |
| Zdroj: | Stochastic Processes and their Applications Stochastic Processes and their Applications, Elsevier, 2021, 142, pp.293-318. ⟨10.1016/j.spa.2021.08.005⟩ |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2021.08.005 |
| Popis: | Let ( g n ) n ⩾ 1 be a sequence of independent and identically distributed random elements of the general linear group G L d ( R ) , with law μ . Consider the random walk G n : = g n … g 1 . Denote respectively by ‖ G n ‖ and ρ ( G n ) the operator norm and the spectral radius of G n . For log ‖ G n ‖ and log ρ ( G n ) , we prove moderate deviation principles under exponential moment and strong irreducibility conditions on μ ; we also establish moderate deviation expansions in the normal range [ 0 , o ( n 1 / 6 ) ] and Berry–Esseen bounds under the additional proximality condition on μ . Similar results are found for the couples ( X n x , log ‖ G n ‖ ) and ( X n x , log ρ ( G n ) ) with target functions, where X n x : = G n ⋅ x is a Markov chain and x is a starting point on the projective space P ( R d ) . |
| Databáze: | OpenAIRE |
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