Random Summation - Boris V. Gnedenko, Victor Yu. Korolev

Random Summation

Limit Theorems and Applications
Buch | Softcover
288 Seiten
2020
CRC Press (Verlag)
978-0-367-44862-2 (ISBN)
73,55 inkl. MwSt
This book focuses on the foundations of the theory of random summation with a description of widespread possibilities of its application to solving important practical problems. It describes the influence of the randomness of the number of summands on the limit behavior of sums of random variables.
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.

Gnedenko, Boris V. | Korolev, Victor Yu.

Examples. Doubling with Repair. Limit Theorems for "Growing" Random Sums. Limit Theorems for Random Sums in the Double Array Scheme. Mathematical Theory of Reliability Growth. A Bayesian Approach. Appendix 1: Information Properties of Probability Distributions. Appendix 2: Asymptotic Behavior of Generalized Doubly Stochastic Poisson Processes. Bibliographical Commentary. Index. References.

NTI/Sales Copy

Erscheinungsdatum
Verlagsort London
Sprache englisch
Maße 156 x 234 mm
Gewicht 453 g
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Wirtschaft Volkswirtschaftslehre Ökonometrie
ISBN-10 0-367-44862-9 / 0367448629
ISBN-13 978-0-367-44862-2 / 9780367448622
Zustand Neuware
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