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

The hitting time density for a reflected Brownian motion

Reflected Brownian motion has been played an important role in economics, finance, queueing and many other fields. In this paper, we present the explicit spectral representation for the hitting time density of the reflected Brownian motion with two-sided barriers, and give some detailed analysis on the computational issues. Numerical analysis reveals that the spectral representation is more app...

Hitting a Boundary Point with Reflected Brownian Motion

An explicit integral test involving the reflection angle is given for the reflected Brownian motion in a half-plane to hit a fixed boundary point.

On Brownian Motion in a Fluid with a Plane Boundary

Traps for Reflected Brownian Motion

Consider an open set D ⊂ R, d ≥ 2, and a closed ball B ⊂ D. Let E TB denote the expectation of the hitting time of B for reflected Brownian motion in D starting from x ∈ D. We say that D is a trap domain if supx E TB = ∞. A domain D is not a trap domain if and only if the reflecting Brownian motion in D is uniformly ergodic. We fully characterize the simply connected planar trap domains using a...

Limiting Behaviors for Brownian Motion Reflected on Brownian Motion

Suppose that g(t) and Wt are independent Brownian motions starting from g(0) = W0 = 0. Consider the Brownian motion Yt reflected on g(t), obtained from Wt by the means of the Skorohod lemma. The upper and lower limiting behaviors of Yt are presented. The upper tail estimate on exit time is computed via principal eigenvalue.