Poisson Random Walk for Solving Wave Equations

We reconsider the connection between random walks of Poisson type and wave equations, following M. Kac's approach which was based on the work by S. Goldstein. A scheme for calculating the distribution of the displacement from the origin at an arbitrary time for the random walk with a time dependent intensity is given, and it is applied to three cases. A simple example showing the use of the distribution is given.