1 research outputs found
Asymptotic behavior of the occupancy density for obliquely reflected Brownian motion in a half-plane and Martin boundary
Let be the occupancy density of an obliquely reflected Brownian motion
in the half plane and let (, ) be the polar coordinates of a
point in the upper half plane. This work determines the exact asymptotic
behavior of (, ) as with
(0, ). We find explicit functions a, b, c such that
(, ) a()
b() e --c(). This closes an open problem first stated by
Professor J. Michael Harrison in August 2013. We also compute the exact
asymptotics for the tail distribution of the boundary occupancy measure and we
obtain an explicit integral expression for . We conclude by finding the
Martin boundary of the process and giving all of the corresponding harmonic
functions satisfying an oblique Neumann boundary problem