MD-semigroups, decomposition of point processes, central limit theorems for certain T2-semigroups

ZH-semigroups and MD-semigroups (multiple Delphic semigroups) are defined. It is shown that MD-semigroups possess the same fundamental properties as D.G. Kendall's Delphic semigroups and a convolution semigroup of point processes is an MD-semigroup. Sufficient conditions under which the central limit theorems for ZH-semigroups take place are obtained, another “straight” proof of the central limit theorem for point processes is given, the decomposition and the classification of positive generalized renewal sequences are discussed.