### 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 |
---|---|

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

### Cite this

**Lower functions for asymmetric Lévy processes.** / Wee, In-Suk.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 85, no. 4, pp. 469-488. https://doi.org/10.1007/BF01203165

}

TY - JOUR

T1 - Lower functions for asymmetric Lévy processes

AU - Wee, In-Suk

PY - 1990/12/1

Y1 - 1990/12/1

N2 - Let {Xt} be a ℝ1 process with stationary independent increments and its Lévy measure v be given by v{y:y>x}=x-αL1(x), v{y:y<-x}=x-αL2(x) where L1, L2 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.

AB - Let {Xt} be a ℝ1 process with stationary independent increments and its Lévy measure v be given by v{y:y>x}=x-αL1(x), v{y:y<-x}=x-αL2(x) where L1, L2 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.

UR - http://www.scopus.com/inward/record.url?scp=34249957717&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249957717&partnerID=8YFLogxK

U2 - 10.1007/BF01203165

DO - 10.1007/BF01203165

M3 - Article

AN - SCOPUS:34249957717

VL - 85

SP - 469

EP - 488

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 4

ER -