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Let $\pi$ be the occupancy density of an obliquely reflected Brownian motionin the half plane and let ($\rho$, $\alpha$) be the polar coordinates of apoint in the upper half plane. This work determines the exact asymptoticbehavior of $\pi$($\rho$, $\alpha$) as $\rho$ $\rightarrow$ $\infty$ with$\alpha$ $\in$ (0, $\pi$). We find explicit functions a, b, c such that$\pi$($\rho$, $\alpha$) $\sim$ $\rho$$\rightarrow$$\infty$ a($\alpha$)$\rho$b($\alpha$) e --c($\alpha$)$\rho$. This closes an open problem first stated byProfessor J. Michael Harrison in August 2013. We also compute the exactasymptotics for the tail distribution of the boundary occupancy measure and weobtain an explicit integral expression for $\pi$. We conclude by finding theMartin boundary of the process and giving all of the corresponding harmonicfunctions satisfying an oblique Neumann boundary problem.

Asymptotic behavior of the occupancy density for obliquely reflected Brownian motion in a half-plane and Martin boundary