## Abstract

For a stationary long-range dependent point process N(·) with Palm distribution P^{0}, the Hurst index H ≡ sup{h:lim sup_{t→∞} t^{-2h} var N(0, t] = ∞} is related to the moment index κ ≡ sup{k:E^{0}(T^{k}) < ∞} of a generic stationary interval T between points (E^{0} denotes expectation with respect to P^{0}) by 2H + κ ≥ 3, it being known that equality holds for a stationary renewal process. Thus, a stationary point process for which κ < 2 is necessarily long-range dependent with Hurst index greater than 1/2 . An extended example of a Wold process shows that a stationary point process can be both long-range count dependent and long-range interval dependent and have finite mean square interval length, i.e., E^{0}(T^{2}) < ∞.

Original language | English |
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Pages (from-to) | 1051-1063 |

Number of pages | 13 |

Journal | Advances in Applied Probability |

Volume | 32 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 2000 |