Holder continuity and occupation-time formulas for fBm self-intersection local time and its derivative

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Abstract

We prove joint Holder continuity and an occupation-time formula for the self-intersection local time of fractional Brownian motion. Motivated by an occupation-time formula, we also introduce a new version of the derivative of self-intersection local time for fractional Brownian motion and prove Holder conditions for this process. This process is related to a different version of the derivative of self-intersection local time studied by the authors in a previous work.
Original languageEnglish
Pages (from-to)299-312
Number of pages14
JournalJournal of Theoretical Probability
Volume28
Issue number1
DOIs
Publication statusPublished - 2015

Keywords

  • Intersection local time
  • Fractional Brownian motion
  • Occupation-time formula

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