Cantor set zeros of one-dimensional Brownian motion minus Cantor function

Details Cantor set zeros of one-dimensional Brownian motion minus Cantor function Cantor set zeros of one-dimensional Brownian motion minus Cantor function

2012-03-04

arxiv.org/abs/1203.0753v1

Mathematics

Probability

18 pages

Scientific paper

It was shown by Antunovi\'{c}, Burdzy, Peres, and Ruscher that a Cantor function added to one-dimensional Brownian motion has zeros in the middle $\alpha$-Cantor set, $\alpha \in (0,1)$, with positive probability if and only if $\alpha \neq 1/2$. We give a refined picture by considering a generalized version of middle 1/2-Cantor sets. By allowing the middle 1/2 intervals to vary in size around the value 1/2 at each iteration step we will see that there is a big class of generalized Cantor functions such that if these are added to one-dimensional Brownian motion, there are no zeros lying in the corresponding Cantor set almost surely.

Affiliated with

Also associated with

No associations

Rating

Cantor set zeros of one-dimensional Brownian motion minus Cantor function does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cantor set zeros of one-dimensional Brownian motion minus Cantor function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cantor set zeros of one-dimensional Brownian motion minus Cantor function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-332371