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

2012/08/22 by Jung, Paul, Markowsky, Greg · 1 citation
#60G22 #60J55 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1208.4407

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.

Cited by

• On the exponential integrability of the derivative of intersection and self-intersection local time for fractional Brownian motion and a limit theorem related to the self-intersection local time for fractional Brownian motion

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