A WARNING ABOUT AN INDEPENDENCE PROPERTY RELATED TO
RANDOM BROWNIAN SCALING
Abstract: In this note, which develops a part of our paper [2], we consider independence
properties between Brownian motion, after Brownian scaling on a random interval
and the length of the interval. We indicate three examples for which the Brownian
scaled process is independent of the corresponding length. On the other hand, we discuss a
case where this independence property does not hold and investigate further results for that
example.
2000 AMS Mathematics Subject Classification: 60G40, 60J55, 60J65.
Key words and phrases: Standard Brownian motion, Brownian scaling, excursion, last
zero, first zero, Brownian meander, Bessel processes.