Abstract
Krafft and Schaefer [14] considered a two-parameter Ehrenfest urn model and found then-step transition probabilities using representations by Krawtchouk polynomials. For a special case of the model Palacios [17] calculated some of the expected first-passage times. This note investigates a generalization of the two-parameter Ehrenfest urn model where the transition probabilitiespi,i+1andpi,i+1are allowed to be quadratic functions of the current statei. The approach used in this paper is based on the integral representations of Karlin and McGregor [9] and can also be used for Markov chains with an infinite state space.
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