Allan Gut : Stopped Random Walks - Limit Theorems and Applications

Classical probability theory provides information about random walks after a fixed number of steps. For applications it is more natural to consider random walks evaluated after random number of steps. This book offers a unified treatment of the subject and shows how this theory can be used to prove limit theorems for renewal counting processes, first passage time processes, and certain two-dimensional random walks, and how these results are useful in various applications.