Summary of applications

  • Dmitrii S. Silvestrov
Part of the Probability and its Applications book series (PIA)


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.


Weak Convergence Independent Increment Continuous Distribution Function Shock Process Extremal Process 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag London 2004

Authors and Affiliations

  • Dmitrii S. Silvestrov
    • 1
  1. 1.Department of Mathematics and PhysicsMälardalen UniversityVästeråsSweden

Personalised recommendations