Passage-time moments for positively recurrent Markov chains

Fractional moments of the passage-times are considered for positively recur rent Markov chains with countable state spaces. A criterion of the finitene ss of the fractional moments is obtained in terms of the convergence rate o f the transition probability to the stationary distribution. As an applicat ion it is proved that the passage time of a direct product process of Marko v chains has the same order of the fractional moments as that of the single Markov chain.