Compound Poisson approximation appears naturally in situations where one deals with a large number of rare events. It has important applications in insurance, extreme value theory, reliability theory, mathematical biology, etc. This book synthesizes the most important recent research in the field in a single volume. With an extensive list of references, it will become the standard reference book on the topic. Features: • Provides a comprehensive overview of this rapidly expanding field • Synthesizes the most important research results of recent years • Presents an array of special topics • Provides the reader with a set of tools needed for research and education The book is of interest to researchers and postgraduate students from probability, statistics, and mathematics.
1. Preliminaries
2. Poisson limit theorem
3. Accuracy of Poisson approximation
4. Applications
5. Compound Poisson limit theorem
6. Accuracy of CP approximation: rare events
7. Accuracy of CP approximation: discrete random variables
8. Sums of m-dependent integer-valued random variables
9. Markov Binomial distribution
10. Compound Poisson approximations related to Kolmogorov’s problem
11. Compound Poisson approximation for sequences of random variables
12. Multivariate compound Poisson approximation
13. Compound Poisson process approximation
14. Appendix.
Biography
Vydas Čekanavičius is a Professor of Mathematics at the Institute of Applied Mathematics, Faculty of Mathematics and Informatics, Vilnius University. He is the author of “Approximation Methods in Probability Theory”, Springer, 2016.
Dr S.Y. Novak works at Middlesex University London. He is the author of “Extreme value methods with applications to finance”, Chapman & Hall/CRC Press, 2011.
