Random Summation Limit Theorems and Applications
Auteurs : Gnedenko Boris V., Korolev Victor Yu.
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.
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
Date de parution : 06-2020
15.6x23.4 cm
Thèmes de Random Summation :
Mots-clés :
Distribution Function; renewal processes; Laplace Stieltjes Transform; random summation; Independent Positive Random Variables; mathematical statistics; Independent Nonnegative Random Variables; asymptotic theory; Galton Watson Process; software reliability; Virtual Waiting Time; Maximum Aggregate Loss; Renewal Duration; Classical Risk Process; Reserve Element; Random Sum; Ruin Probability; Nonnegative Random Variable; Proper Distribution Function; Queue’s Release; Particle Arrivals; Characteristic Function; Random Variables; Poisson Flows; Actuarial Mathematics; Functional Iteration; Partial Cross-sections; Secondary Particles; Pollaczek Khinchin Formula; Repair Duration