## Abstract

Criteria are determined for the variance to mean ratio to be greater than one (overdispersed) or less than one (under-dispersed). This is done for random variables which are functions of a Markov chain in continuous time, and for the counts in a simple point process on the line. The criteria for the Markov chain are in terms of the infinitesimal generator and those for the point process in terms of the conditional intensity. Examples include a conjecture of Faddy (1994). The case of time-reversible point processes is particularly interesting, and here underdispersion is not possible. In particular, point processes which arise from Markov chains which are time-reversible, have finitely many states and are irreducible are always overdispersed.

Original language | English |
---|---|

Pages (from-to) | 303-312 |

Number of pages | 10 |

Journal | Journal of Applied Probability |

Volume | 35 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 1998 |

Externally published | Yes |

## Keywords

- Conditional intensity
- Infinitesimal generator
- Markov chain
- Positive and negative correlations
- Transition rates