Summary of applications

Abstract

This chapter gives a summary of applications of general limit theorems on randomly stopped stochastic processes and compositions of stochastic processes. The goal is to show how the general limit theorems given in Chapters 2 and 3 can be applied to some classical models of càdlàg processes with random stopping. These models include randomly stopped sum-processes (random sums), randomly stopped maxprocesses (extremes with random sample size), generalised exceeding processes, and various renewal models, namely sum-processes and max-processes with renewal stopping and the so-called shock models. We also consider some related models, for example accumulation processes.