Imagine a symmetric random walk on a finite 2D grid $(m \times n)$ starting at $(x_0,y_0)$ taking steps either up, down, left, or right with equal chance. If there is a reflection on the boundary then what is the expected hitting time for a rectangular subset $(n-a) \times (m-b)$ in the 'corner' of the grid.
Edit: and what is the probability of hitting this subset in number of steps t?