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

Paul Jung and Greg Markowsky ()
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Paul Jung: University of Alabama
Greg Markowsky: Monash University

Journal of Theoretical Probability, 2015, vol. 28, issue 1, 299-312

Abstract: 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; 60G22; 60J55 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-012-0474-8

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