This monograph serves as an introductory text to classical renewal theory and some of its applications for graduate students and researchers in mathematics and probability theory. Renewal processes play an important part in modeling many phenomena in insurance, finance, queuing systems, inventory control and other areas. In this book, an overview of univariate renewal theory is given and renewal processes in the non-lattice and lattice case are discussed. A pre-requisite is a basic knowledge of probability theory.

Covers contemporary results on the main topics of renewal theory Presents all results in a detailed and consistent manner, thus providing a step-by-step introduction to renewal theory Includes new applications as well as a special section on multivariate renewal theory and renewal reward processes Includes supplementary material: sn.pub/extras

Autorentext

Kosto V. Mitov is a Professor at the Aviation Faculty of the National Military University Vasil Levski, Bulgaria. He gives courses in probability theory and applied mathematics and his research interests include the theory of branching processes and renewal theory. He has published many research papers on branching stochastic processes, renewal processes, extreme value theory and distribution theory.

Edward Omey is a Professor at the Faculty of Economics and Business of the KU Leuven Campus Brussels. He gives courses in statistics and econometrics and his research interests include regular variation and its applications in probability theory. He has published many research papers on renewal theory and extreme value theory, and also several didactical papers on specific topics in mathematics and probability.

Inhalt
Preface.- Renewal Processes.- Discrete Time Renewal Processes.- Extensions and Applications.- Appendix: Convolutions and Laplace Transforms.