ON A GENERALIZATION OF THE EHRENFEST URN MODEL

Krafft and Schaefer [14] considered a two-parameter Ehrenfest urn mode l and found the n-step transition probabilities using representations by Krawtchouk polynomials, For a special case of the model Palacios [1 7] calculated some of the expected first-passage times. This note inve stigates, a generalization of the two-parameter Ehrenfest urn model wh ere the transition probabilities p(i,i+1) and p(i,i-1) are allowed to be quadratic functions of the current state i. The approach used in th is paper is based on the integral representations of Karlin and McGreg or [9] and can also be used for Markov chains with an infinite state s pace.