Laws of the iterated logarithm for symmetric stable processes

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11 Scopus citations


Let X(t) be a symmetric stable process of index α> 1 with local time L(t, x) and define R(t)=|{x:X(s)=x for some s≦t}| and L*(t) = sup{L(t, x): x∈ℝ1}. We prove that {Mathematical expression} where c1, c2∈(0, ∞). A law of the iterated logarithm is also given for X(t) when its large jumps are excluded.

Original languageEnglish (US)
Pages (from-to)271-285
Number of pages15
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Issue number3
StatePublished - Sep 1985
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • General Mathematics


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