Properties of the Invariant Measure and Applications

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


The main result to be proved in this chapter is that under suitable hypotheses, the μ-invariant distribution v on P(ℝd) satisfies for some α > 0
$$ {\int {\left| {\frac{{\left\| x \right\|}}{{ < x,y > }}} \right|} ^\alpha }dv(\overline {x)} < \infty $$


Probability Measure Lyapunov Exponent Invariant Measure Random Matrix Hausdorff Dimension 


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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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