The law of the iterated logarithm for local time of a Lévy process

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Abstract

Let {Xt} be a one-dimensional Lévy process with local time L(t, x) and L*(t)=sup{L(t, x): x ∈ ℝ}. Under an assumption which is more general than being a symmetric stable process with index α>1, we obtain a LIL for L*(t). Also with an additional condition of symmetry, a LIL for range is proved.

Original languageEnglish
Pages (from-to)359-376
Number of pages18
JournalProbability Theory and Related Fields
Volume93
Issue number3
DOIs
Publication statusPublished - 1992 Sep 1

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ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Statistics and Probability

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