A01=Boris V. Gnedenko
A01=Victor Yu. Korolev
Actuarial Mathematics
actuarial risk analysis
advanced limit theorem applications
asymptotic theory
Author_Boris V. Gnedenko
Author_Victor Yu. Korolev
Bayesian probability methods
Category=PBT
Category=PBWL
Characteristic Function
Classical Risk Process
convergence criteria
Distribution Function
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Functional Iteration
Galton Watson Process
Independent Nonnegative Random Variables
Independent Positive Random Variables
Laplace Stieltjes Transform
mathematical statistics
Maximum Aggregate Loss
Nonnegative Random Variable
Partial Cross-sections
Particle Arrivals
Poisson Flows
Pollaczek Khinchin Formula
probability theory applications
Proper Distribution Function
Queue's Release
Queue’s Release
Random Sum
random summation
Random Variables
reliability engineering systems
Renewal Duration
renewal processes
Repair Duration
Reserve Element
Ruin Probability
Secondary Particles
software reliability
stochastic modeling
Virtual Waiting Time
Product details
- ISBN 9780849328756
- Weight: 690g
- Dimensions: 156 x 234mm
- Publication Date: 27 Mar 1996
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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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.
