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Transformation de Lévy et zéros du mouvement Brownien (1995)

Malric, M.

Springer

Probability theory and related fields 101 (1995), S. 227-236

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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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