Random Summation: Limit Theorems and Applications

This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the distribution of stock prices or surplus processes. General mathematical theory of reliability growth of modified systems, including software, is presented. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions, and asymptotic behavior of doubly stochastic Poisson processes. Random Summation: Limit Theorems and Applications will be of use to specialists and students in probability theory, mathematical statistics, and stochastic processes, as well as to financial mathematicians, actuaries, and to engineers desiring to improve probability models for solving practical problems and for finding new approaches to the construction of mathematical models.Additional ISBNs0849328756, 1003067891, 0367448629, 9780849328756, 9781003067894, 9780367448622Random Summation: Limit Theorems and Applications 1st Edition is written by Boris V. Gnedenko; Victor Yu. Korolev and published by CRC Press. ISBNs for Random Summation are 9781000141177, 1000141179 and the print ISBNs are 9780849328756, 0849328756. Additional ISBNs include 0849328756, 1003067891, 0367448629, 9780849328756, 9781003067894, 9780367448622.