DENSITY OF PATHS OF ITERATED LEVY TRANSFORMS OF BROWNIAN MOTION

被引：2
|
作者：
Malric, Marc
机构：
来源：
ESAIM-PROBABILITY AND STATISTICS | 2012年 / 16卷
关键词：
Brownian motion; Levy transform; excursions; zeroes of Brownian motion; ergodicity;
D O I：
10.1051/ps/2011020
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
The Levy transform of a Brownian motion B is the Brownian motion B-(1) given by B-t((1)) = integral(t)(0)sgn(B-s) dB(s); call B-(n) the Brownian motion obtained from B by iterating n times this transformation. We establish that almost surely, the sequence of paths (t (sic) B-t((n)))(n >= 0) is dense in Wiener space, for the topology of uniform convergence on compact time intervals.
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页码：399 / 424
页数：26
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