On the semimartingale representation of reflecting Brownian motion in a cusp (Q1326330)

Let \(C\) be the symmetric cusp \(\{(x,y) \in \mathbb{R}^ 2:-x^ \beta \leq y \leq x^ \beta\), \(x \geq 0\}\) where \(\beta>1\). We decide whether or not reflecting Brownian motion in \(C\) 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.