### Abstract

We introduce an increasing set of classes Ga (0a1) of infinitely divisible (i.d.) distributions on {0,1,2,…}, such that G0 is the set of all compound-geometric distributions and G1 the set of all compound-Poisson distributions, i.e. the set of all i.d. distributions on the non-negative integers. These classes are defined by recursion relations similar to those introduced by Katti [4] for G1 and by Steutel [7] for G0. These relations can be regarded as generalizations of those defining the so-called renewal sequences (cf. [5] and [2]). Several properties of i.d. distributions now appear as special cases of properties of the Ga'.

Original language | English |
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Pages (from-to) | 47-55 |

Number of pages | 9 |

Journal | Stochastic Processes and their Applications |

Volume | 5 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1977 |

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## Cite this

Harn, van, K., & Steutel, F. W. (1977). Generalized renewal sequences and infinitely divisible lattice distributions.

*Stochastic Processes and their Applications*,*5*(1), 47-55. https://doi.org/10.1016/0304-4149(77)90049-7