Incorporating a collection of recent results, **PΓ³lya Urn Models deals with discrete probability through the modern and evolving urn theory and its numerous applications.
The book first substantiates the realization of distributions with urn arguments and introduces several modern tools, including exchangeability and stochastic processes via urns. It reviews classical probability problems and presents dichromatic PΓ³lya urns as a basic discrete structure growing in discrete time. The author then embeds the discrete PΓ³lya urn scheme in Poisson processes to achieve an equivalent view in continuous time, provides heuristical arguments to connect the PΓ³lya process to the discrete urn scheme, and explores extensions and generalizations. He also discusses how functional equations for moment generating functions can be obtained and solved. The final chapters cover applications of urns to computer science and bioscience.
Examining how urns can help conceptualize discrete probability principles, this book provides information pertinent to the modeling of dynamically evolving systems where particles come and go according to governing rules.**