Abstract
In this paper, it is shown that the iterated Lévy transforms (β n) of a standard Brownian motion β, so defined:
satisfy the following property: a.s.,β n andβ m have common zeros, as soon asm>n+1. This property bears some relation with the conjectured ergodicity of the Lévy transform.
Référence
Dubins, L., Smorodinsky, M.: The Modified, discrete, Lévy transformation is Bernoulli. In: Azéma, J., Meyer, P.A. (eds.) Sém. Probas.XXVI. (Lect. Notes Math. vol., 1526 pp. 157–161) Berlin Heidelberg New York: Springer 1992
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Malric, M. Transformation de Lévy et zéros du mouvement Brownien. Probab. Th. Rel. Fields 101, 227–236 (1995). https://doi.org/10.1007/BF01375826
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DOI: https://doi.org/10.1007/BF01375826
Mathematics Subject Classification
- 60H05
- 60I65