Some Properties of the Delayed Renewal Sequence Semigroup

A sequence （v_n, n ≥ 1） is called a delayed renewal sequence if and only if it is a transition probability sequence （p_ij（n）, n ≥ 1） of a Markov chain for some i and j. In this paper, we prove that the delayed renewal sequence semigroup has property ILID （that is, an infinitesimal array limit is infinitely devisible）, and that the.semigroup of positive delayed renewal sequences is a Delphic semigroup.