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