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Journal of Theoretical Probability

, Volume 28, Issue 1, pp 299–312 | Cite as

Hölder Continuity and Occupation-Time Formulas for fBm Self-Intersection Local Time and Its Derivative

  • Paul Jung
  • Greg Markowsky
Article

Abstract

We prove joint Hölder 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 Hölder 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.

Keywords

Intersection local time Fractional Brownian motion  Occupation-time formula 

Mathematics Subject Classification (2010)

60G22 60J55 

Notes

Acknowledgments

We thank Yimin Xiao for helpful comments. The second author was supported by Australian Research Council Grant DP0988483.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AlabamaBirminghamUSA
  2. 2.Department of MathematicsMonash UniversityClaytonAustralia

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