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  • 60H05  (1)
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    Electronic Resource
    Electronic Resource
    Transformation de Lévy et zéros du mouvement Brownien (1995)
    Springer
    Probability theory and related fields 101 (1995), S. 227-236 
    Details
    ISSN: 1432-2064
    Keywords: 60H05 ; 60I65
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, it is shown that the iterated Lévy transforms (β n ) of a standard Brownian motion β, so defined: $$\beta ^0 = \beta ,and:\beta _t^{n + 1} = \int\limits_0^t {\operatorname{sgn} (\beta _s^n )} d\beta _s^n (n \geqq 0)$$ 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01375826
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