Sharp Integrability for Brownian Motion in Parabola-shaped Regions

Rodrigo Banuelos, Tom Carroll

We study the sharp order of integrability of the exit position of Brownian motion from the planar domains ${\cal P}_α= \{(x,y)\in \bR\times \bR\colon x> 0, |y| < Ax^α\}$, $0<\alpha <1$.…