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Invariance principles for the empirical measure of a mixing sequence and for the local time of markov processes

  • P. Doukhan
  • J. R. Leon
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1193)

Abstract

We show an invariance principle for the empirical measure of a stationary strongly mixing sequence indexed by the unit ball of some Sobolev space Hs. We also obtain invariance principle and law of iterated logarithm for the local time of Markov processes indexed by Hs.

We note that the regularity condition s > d/2 in the first framework for random variables with values in a compact riemannian manifold E becomes s > d/2-1 in the continuous case of the brownian motion on E.

Keywords

Brownian Motion Markov Process Invariance Principle Empirical Measure Iterate Logarithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • P. Doukhan
    • 1
  • J. R. Leon
    • 2
  1. 1.U.A. CNRS 743 "Statistique Appliquée"Université Paris-SudOrsayFrance
  2. 2.Departamentado de MatematicasUniversidad Central de Venezuela Facultad de CienciasCaracasVenezuela

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