Abstract
LetC be the symmetric cusp {(x, y)∈ℝ2:−x β≦y≦x β,x≧0} where β>1. In this paper we decide whether or not reflecting Brownian motion inC has a semimartingale representation. Here the reflecting Brownian motion has directions of reflection that make constant angles with the unit inward normals to the boundary. Our results carry through for a wide class of asymmetric cusps too.
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