On the Exactness of the Lévy-Transformation
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.
KeywordsContinuous Function Stochastic Process Probability Measure Probability Theory Measurable Function
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.
- 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:1206.2485Google Scholar