Comparison of Lyapunov Exponents and Boundaries

  • Philippe Bougerol
  • Jean Lacroix
Part of the Progress in Probability and Statistics book series (PRPR, volume 8)


In the preceding chapter we have given a criterion ensuring that the two upper Lyapunov exponents are distinct. It will give us all we need for the study of limit theorems. But a sharp study of the behaviour at infinity of the random products S requires a precise knowledge of the relations between all the exponents. For instance they provide all the limit values of \( \frac{1}{n}\;Log\;\left\| {{S_{n}}\left( \omega \right)x} \right\| \) , when ω is kept fixed and x runs through ℝd (Osseledec’s theorem) and determine the possible boundaries towards which Sn converges.


Probability Measure Lyapunov Exponent Closed Subgroup Invariant Distribution Invariant Probability Measure 
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Copyright information

© Birkhäuser Boston, Inc. 1985

Authors and Affiliations

  • Philippe Bougerol
    • 1
  • Jean Lacroix
    • 2
  1. 1.UER de MathématiquesUniversité Paris 7ParisFrance
  2. 2.Département de MathématiquesUniversité de Paris XIIIVilletaneuseFrance

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