2015/07/10 by Silvius Klein, Pedro Duarte, Klein, Silvius +1
Mathematics · Decision Sciences · #Stochastic processes and statistical mechanics #Probability and Risk Models #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1507.02969
In this paper we prove the continuity of all Lyapunov exponents, as well as the continuity of the Oseledets decomposition, for a class of irreducible cocycles over strongly mixing Markov shifts. Moreover, gaps in the Lyapunov spectrum lead to a Hölder modulus of continuity for these quantities. This result is an application of the abstract continuity theorems obtained in [4], and generalizes a theorem of E. Le Page on the Hölder continuity of the maximal LE for one-parameter families of strongly irreducible and contracting cocycles over a Bernoulli shift. This is a draft of a chapter in our forthcoming research monograph [4].