ABSTRACT

Incorporating a collection of recent results, Polya Urn Models deals with discrete probability through the modern and evolving urn theory and its numerous applications. It looks at how some classical problems of discrete probability have roots in urn models. The book covers the Polya-Eggenberger, Bernard Friedman's, the Bagchi-Pal, and the Ehrenfest urns. It also explains the processes of poissonization and depoissonization and presents applications to random trees, evolution, competitive exclusion, epidemiology, clinical trials, and random circuits. The text includes end-of-chapter exercises that range from easy to challenging, along with solutions in the back of the book.

chapter 2|10 pages

Some Classical Urn Problems

chapter 3|24 pages

Po´lya Urn Models

chapter 4|18 pages

Poissonization

chapter 5|12 pages

The Depoissonization Heuristic

chapter 6|18 pages

Urn Schemes with Random Replacement

chapter 7|18 pages

Analytic Urns

chapter 9|38 pages

Urn Schemes in Bioscience

chapter 10|18 pages

Urns Evolving by Multiple Drawing