Random Summation: Limit Theorems and Applications

Examples Examples Related to Generalized Poisson Laws A Remarkable Formula of Queueing Theory Other Examples Doubling with Repair Mathematical Model A Limit Theorem for the Trouble-Free Performance Duration The Class of Limit Laws Some Properties of Limit Distributions Domains of Geometrical Attraction of the Laws from Class c Limit Theorems for "Growing" Random Sums A Transfer Theorem. Limit Laws Necessary and Sufficient Conditions for Convergence Convergence to Distributions from Identifiable Families Limit Theorems for Risk Processes Some Models of Financial Mathematics Rarefied Renewal Processes Limit Theorems for Random Sums in the Double Array Scheme Transfer Theorems. Limit Laws Converses of the Transfer Theorems Necessary and Sufficient Conditions for the Convergence of Random Sums of Independent Identically Distributed Random Variables More on Some Models of Financial Mathematics Limit Theorems for Supercritical Galton-Watson Processes Randomly Infinitely Divisible Distributions Mathematical Theory of Reliability Growth. A Bayesian Approach Bayesian Reliability Growth Models Conditionally Geometrical Models Conditionally Exponential Models Renewing Models Models with Independent Decrements of Volumes of Defective Sets Order-Statistics-Type (Mosaic) Reliability Growth Models Generalized Conditionally Exponential Models Statistical Prediction of Reliability by Renewing Models Statistical Prediction of Reliability by Order-Statistics-Type Models Appendix 1: Information Properties of Probability Distributions Mathematical Models of Information and Uncertainty Limit Theorems of Probability Theory and the Universal Principle of Non-Decrease of Uncertainty Appendix 2: Asymptotic Behavior of Generalized Doubly Stochastic Poisson Processes General Information on Doubly Stochastic Poisson Processes A General Limit Theorem for Superpositions of Random Processes Limit Theorem for Cox Processes Limit Theorems for Generalized Cox Processes Convergence Rate Estimates in Limit Theorems for Generalized Cox Processes Asymptotic Expansions for Generalized Cox Processes Estimates for the Concentration Functions of Generalized Cox Processes Bibliographical Commentary Index References