Passage time moments for multidimensional diffusions

Let tau(r) denote the hitting time of B(0 : r) for a multidimensional diffu sion process. We give verifiable criteria for finiteness/infiniteness of E- x(tau(r)(p)). As an application we exhibit classes of diffusion processes w hich are recurrent but E-x(tau(r)(P)) is infinite For All p > 0, \x\ > r > 0; this includes the two-dimensional Brownian motion and the reflecting Bro wnian motion In a wedge with a certain parameter alpha = 0.