  We propose a discrete analogue for the boundary local time of reflected
diffusions in bounded Lipschitz domains. This discrete analogue, called the
discrete local time, can be effectively simulated in practice and is obtained
pathwise from random walks on lattices. We establish weak convergence of the
joint law of the discrete local time and the associated random walks as the
lattice size decreases to zero. A cornerstone of the proof is the local central
limit theorem for reflected diffusions developed in [7]. Applications of the
join convergence result to PDE problems are illustrated.
