REFLECTED BROWNIAN-MOTION IN A CONE - SEMIMARTINGALE PROPERTY

In this paper, the object of study is reflected Brownian motion in a cone in d-dimensions (d greater than or equal to 3) with nonconstant oblique reflection on each radial line emanating from the vertex of the cone. The basic question considered here is ''When is this process a semimartingale?''. Conditions for the existence and uniqueness of the process for which the vertex is an instantaneous state were given by Kwon, which is resolved in terms of a real parameter alpha(infinity) depending on the cone and the direction of reflection. It is shown that starting from any point of the cone, the process is a semimartingale if alpha(infinity) < 1, alpha(infinity) not equal 0 and not a semimartingale if 1 < alpha(infinity) < 2.