Let b(t) be brownian motion. Define r(t) by
r(0)=a>0, dr(t)=db(t) except when r(t)=0,, where r reflects,
-and when r(t)=max{r(s):s It is well known that the distribution of
brownain local time at zero, up to time one, has the
distribution of the the absolute value of a standard normal
variable. I will show that the distribution of the local
time on the graph of a smooth increasing function on
[0,1] is distributionally smaller than twice this local
time at zero, and that this "twice" may not be replaced with
a smaller multiple.
Talk 2:
Title: Distribution of brownian local time on curves