Hitting time of a corner for a reflected diffusion in the square

We investigate the expectation of the hitting time of a neighborhood of the origin for a two dimensional reflected diffusion in the unit square. More specifically, we distinguish three different regimes depending on the sign of the correlation coefficient of the diffusion matrix at the point 0. For a positive correlation coefficient, the expectation of the hitting time is uniformly bounded as the neighborhood shrinks. For a negative one, the expectation explodes in a polynomial way as the diameter of the neighborhood vanishes. In the null case, the expectation explodes in a logarithmic rate. From a practical point of view, the considered hitting time appears as a deadlock time in various resource sharing problems.