The First Exit Time of Planar Brownian Motion from The Interior Of a Parabola

By Rodrigo Bañuelos, R. Deblassie, R. Smits. 2001

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Symmetric Stable Processes in Cones (2004, background): “In addition to generalized cones, the above limits have been studied in [ 3 , 34, 28, 29] in the case of Brownian motion in parabolas and in other parabolic regions of the form D ={ (x, y) ∈ R × R d−1 : x> 0, |y| <A x p },”
Torsional Rigidity and Expected Lifetime of Brownian Motion (2002, background): “29) These regions are generalizations of those in papers [5, 10] where the exact order of integrability of the lifetime is studied.”
The first exit time of Brownian motion from a parabolic domain (2002, background): “As pointed out in Bañuelos et al. (2001), it is a highly non-trivial matter to find other unbounded domains above graphs of functions for which one can say something deep about the (tail) distribution of D.”
Neumann and Dirichlet Heat Kernels in Inner Uniform Domains (2011, result): “Some results are contained in the work of Banũelos et al [9].”