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

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## 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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