Symmetric Lévy Processes on Nilpotent Groups

This chapter anticipates on later results that show how the limit theorems of Chaps. 5 and 6 apply to certain long-range random walks. It focuses on the problem of identifying the limit Lévy process that is obtained through these limit theorems when applied to a given explicit long-range random walk. This is done by drawing interesting links between variations on established results regarding approximations of Lévy processes on Lie groups on the one hand and the limit theorems obtained in Chaps. 5 and 6 on the other hand. Several examples are given to illustrate the limit theorems explicitly using this approach. Examples discussed in Chap. 1 are also revisited in this new light.