Obliquely reflected Brownian motion in nonsmooth planar domains

Conditioned Brownian motion in planar domains

We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains. Short title: Conditioned Brownian motion AMS Subject Classification (1985): Primary 60J50; Secondary 60J45, 60J65

On the exit distribution of partially reflected Brownian motion in planar domains

We show that the dimension of the exit distribution of planar partially reflected Brownian motion can be arbitrarily close to 2.

Heat Equation and Reflected Brownian Motion in Time Dependent Domains

Transcience/recurrence for Normally Reflected Brownian Motion in Unbounded Domains

Let D ( R be an unbounded domain and let B(t) be a Brownian motion in D with normal reflection at the boundary. We study the transcience/recurrence dichotomy, focusing mainly on domains of the form D = {(x, z) ∈ R : |z| < H(|x|)}, where d = l + m and H is a sufficiently regular function. This class of domains includes various horn-shaped domains and generalized slab domains.

Weak Approximation of Obliquely Reflected Diffusions in Time-dependent Domains

In an earlier paper, we proved the existence of solutions to the Skorohod problem with oblique reflection in time-dependent domains and, subsequently, applied this result to the problem of constructing solutions, in time-dependent domains, to stochastic differential equations with oblique reflection. In this paper we use these results to construct weak approximations of solutions to stochastic ...