Exit time from a positive quadrant for a two-dimensional Markov chain

The paper tends to elucidate relationship between independent work of J.W. Cohen and that of A.O. Pittenger and L.A. Klein-Haneveld on the mean of the first exit time from a positive quadrant in a two-dimensional random walk. In order to make comparison more transparent-and at the same time to introduce some novelty-a two-dimensional Markov chain in a continuous time is taken as a frame of reference. The paper concentrates on those aspects of both approaches which have common roots in the Markov chain theory and the associated Martingales.