Polya Urn Models (Hardcover)

Urn Models and Rudiments of Discrete Probability
Probability Axioms
Random Variables
Independence of Discrete Random Variables
Realization of Basic Discrete Distributions via Urns
The Poisson Process
Markov Chains
Exchangeability
Some Classical Urn Problems
Ballot Problems
Occupancy Problems
Coupon Collector’s Problems
The Gambler’s Ruin
Banach’s Matchbox Problem
Polya Urn Models
Tenability
The Polya?Eggenberger Urn
Bernard Friedman’s Urn
The Bagchi?Pal Urn
The Ehrenfest Urn
Poissonization
The Polya Process
Poissonization of Multicolor Deterministic Schemes
The Deterministic Monochromatic Polya Process
The Polya?Eggenberger Process
The Ehrenfest Process
Poissonization of Schemes with Random Entries
The Depoissonization Heuristic
Depoissonization of Dichromatic Polya Processes
Depoissonization of Invertible Processes
Depoissonization Examples
Urn Schemes with Random Replacement
Martingales
Extended Urn Schemes
Deterministic Dichromatic Extended Urn Schemes
Dichromatic Extended Urn Schemes with Random Entries
Extended Multicolor Urn Schemes
Analytic Urns
Enumerating Histories in Balanced Schemes
Analytic Urn Examples
Applications of Polya Urns in Informatics
Search Trees
Recursive Trees
Urn Schemes in Bioscience
Evolution of Species
Competitive Exclusion
Epidemiology: Kriz’ Polytonomous Urn Scheme
Clinical Trials
Urns Evolving by Multiple Drawing
Urns Evolving by Drawing Pairs of Balls
The Chen?Wei Urn
Linear Rectangular Urns
Application of Rectangular Schemes in Random Circuits
Answers to Exercises
Notation
Bibliographic Notes
Bibliography
Index
Exercises appear at the end of each chapter.