Random Summation: Limit Theorems and Applications - Hardcover

Gnedenko, Boris V.; Korolev, Victor Yu.

Hardcover

ISBN 10: 0849328756 ISBN 13: 9780849328756

Publisher: CRC Press, 1996

Synopsis

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.

About this title

About the Author

Gnedenko\, Boris V.; Korolev\, Victor Yu.

From the Back Cover

We intended not only to bring the reader up to date on recent results and foundations of the theory describing the influence of the randomness of the number of summands on the limit behavior of sums of random variables, but also to demonstrate the potentialities of probability theory in solving important applied problems, especially those which at first sight seem to have no mathematically strict solutions.

Edition details

• Publisher: CRC Press
• Publication date: 1996
• Language: English
• ISBN 10: 0849328756
• ISBN 13: 9780849328756
• Binding: Hardcover
• Edition number: 1
• Number of pages: 288