### Abstract

Let {X_{t}} be a ℝ^{1} process with stationary independent increments and its Lévy measure v be given by v{y:y>x}=x^{-αL}_{1}(x), v{y:y<-x}=x^{-αL}_{2}(x) where L_{1}, L_{2} are slowly varying at 0 and ∞ and 0<α≦1. We construct two types of a nondecreasing function h(t) depending on 0<α<1 or α=1 such that lim inf {Mathematical expression} a.s. as t→ 0 and t→∞ for some positive finite constant C.

Original language | English |
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Pages (from-to) | 469-488 |

Number of pages | 20 |

Journal | Probability Theory and Related Fields |

Volume | 85 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1990 Dec 1 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Statistics and Probability