Markoff chains with an enumerable number of states and a class of cascade processes

In § 1 a Markoff chain is defined, and a theorem of Kolmogoroff relating to its asymptotic behaviour is stated. Its stable distributions are examined in § 2 and some further results are obtained. These are then applied in §§ 3, 4 to a certain generalization of the cascade process, regarded as a Markoff chain with a special kind of matrix.