On generalized Polya urn models

We consider a general two-color urn model characterized by a 2 x 2 matrix of integers [GRAPHICS] without constraints on the values of these four integers other than non-negativity. Exact distributions of the number of balls of a specific color that appear after n draws are presented. Via Poissonization, we obtain an asymptotic mean for a specific example to illustrate that asymptotics of bona fide nature may appear in non-classical urn models. (C) 2000 Published by Elsevier Science B.V. All rights reserved.