We consider central limit theory for urn models in which balls are not necessarily replaced after being drawn, giving rise to negative diagonal entries in the generating matrix. Under conditions on the eigenvalues and eigenvectors, we give results both for the contents of the urn and the number of times balls of each type are drawn.
Smythe, R. T. (1996). Central limit theorems for urn models. Stochastic Processes and Their Applications, 65(1), 115–137. https://doi.org/10.1016/S0304-4149(96)00094-4