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On the Exactness of the Lévy-Transformation

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Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 2123)

Abstract

In a recent paper we gave a sufficient condition for the strong mixing property of the Lévy-transformation. In this note we show that it actually implies a much stronger property, namely exactness.

Keywords

  • Continuous Function
  • Stochastic Process
  • Probability Measure
  • Probability Theory
  • Measurable Function

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References

  1. V. Prokaj, Some Sufficient Conditions for the Ergodicity of the Lévy-Transformation, ed. by C. Donati-Martin, A. Lejay, A. Rouault. Séminaire de Probabilités, XLV (Springer, New York, 2013), pp. 93–121. Doi: 10.1007/978-3-319-00321-4_2, arxiv:1206.2485

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Acknowledgements

The author thanks Michel Emery for reading the first version of this note and offering helpful comments, and the referee for suggesting a simplification in the proof of Proposition 3.

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Correspondence to Vilmos Prokaj .

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© 2014 Springer International Publishing Switzerland

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Prokaj, V. (2014). On the Exactness of the Lévy-Transformation. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLVI. Lecture Notes in Mathematics(), vol 2123. Springer, Cham. https://doi.org/10.1007/978-3-319-11970-0_16

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