Distributions in the constant-differentials Pólya process

Published in Statistics & Probability Letters, 2019

Recommended citation: Mahmoud, H. M. and Zhang, P. (2020). "Distributions in the constant-differentials Pólya process." Statistics & Probability Letters, 156, 108592. https://doi.org/10.1016/j.spl.2019.108592

We study a class of unbalanced constant-differentials Pólya processes on white and blue balls. We show that the number of white balls, the number of blue balls, and the total number of balls, when appropriately scaled, all converge in distribution to gamma random variables with parameters depending on the differential index and the amount of ball addition at the epochs, but not on the initial conditions. The result is obtained by an analytic approach utilizing partial differential equations. We present a martingale formulation that may provide alternatives.


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