Joint densities for random walks in the plane (Q1117591)

We point out the existence of computationally convenient techniques for calculating the joint probability density for the position of a Pearson random walk after n steps. A new Fourier-Bessel function expansion for \(p_ n(r,\theta)\) is developed for this purpose which does not require radial symmetry, but does require that \(p_ n(r,\theta)=0\) when r exceeds some maximum radius, R.