The Polya Urn Process and the Stochastic Approximation of Its Behavior

This paper begins by describing the Polya urn process. Next, distributions of ball counts and ball proportions are derived. These derivations should provide the reader with an understanding of how urn processes behave. After this intuition is developed, a stochastic approximation of the process is derived. This way, the relationship between the stochastic results and the previously derived results is clear. Finally, a case where the assumptions of stochastic approximation may not hold is introduced and an alternative solution is described.