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

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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

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© 1986 Springer-Verlag

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Doukhan, P., Leon, J.R. (1986). Invariance principles for the empirical measure of a mixing sequence and for the local time of markov processes. In: Fernique, X., Heinkel, B., Meyer, PA., Marcus, M.B. (eds) Geometrical and Statistical Aspects of Probability in Banach Spaces. Lecture Notes in Mathematics, vol 1193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077096

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  • DOI: https://doi.org/10.1007/BFb0077096

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16487-6

  • Online ISBN: 978-3-540-39826-4

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