Abstract
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.
Keywords
- Point Process
- Central Limit Theorem
- Simple Factor
- Triangular Array
- Convolution Semigroup
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© 1989 Springer-Verlag
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He, Y. (1989). MD-semigroups, decomposition of point processes, central limit theorems for certain T2-semigroups. In: Heyer, H. (eds) Probability Measures on Groups IX. Lecture Notes in Mathematics, vol 1379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087849
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DOI: https://doi.org/10.1007/BFb0087849
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