Lower functions for asymmetric Lévy processes

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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.

Original languageEnglish
Pages (from-to)469-488
Number of pages20
JournalProbability Theory and Related Fields
Issue number4
Publication statusPublished - 1990 Dec 1


ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Statistics and Probability

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