Classical probability theory provides information about random walks
after a fixed number of steps. For applications, however, it is more
natural to consider random walks evaluated after a random number of
steps. Examples are sequential analysis, queuing theory, storage and
inventory theory, insurance risk theory, reliability theory, and the
theory of contours. Stopped Random Walks: Limit Theorems and
Applications shows how this theory can be used to prove limit theorems
for renewal counting processes, first passage time processes, and
certain two-dimenstional random walks, and to how these results are
useful in various applications.
This second edition offers updated content and an outlook on further
results, extensions and generalizations. A new chapter examines
nonlinear renewal processes in order to present the analagous theory for
perturbed random walks, modeled as a random walk plus "noise."