Probability Seminar - Xiaochuan Yang

Institution: Michigan State University
Title: An invitation to large scale sojourn properties of Brownian motion
Date: Thursday, January 25, 2018
Location: C405 Wells Hall
Time: 3:00 PM - 3:50 PM

For a one dimensional Brownian motion, we consider the sets of times where Brownian motion stays inside some moving boundaries. The boundaries considered are power functions with the power in [0, 1/2].  Since the usual scaling for Brownian motion at time t is square root of t,  the sojourn sets we considered describe the recurrence of a Brownian motion around zero.  We give large scale geometric properties of these sets using macroscopic dimensions introduced by Barlow and Taylor in the late 80's.  The audience of 881/882 might find this talk interesting.