Fractional Brownian Density Process and Its Self-Intersection Local Time of Order k

T. Bojdecki (), L. G. Gorostiza () and A. Talarczyk ()
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T. Bojdecki: University of Warsaw
L. G. Gorostiza: Centro de Investigación y de Estudios Avanzados
A. Talarczyk: University of Warsaw

Journal of Theoretical Probability, 2004, vol. 17, issue 3, 717-739

Abstract: Abstract The fractional Brownian density process is a continuous centered Gaussian $$S$$ ′(ℝ d )-valued process which arises as a high-density fluctuation limit of a Poisson system of independent d-dimensional fractional Brownian motions with Hurst parameter H. ( $$S$$ ′(ℝ d ) is the space of tempered distributions). The main result proved in the paper is that if the intensity measure μ of the (initial) Poisson random measure on ℝ d is either the Lebesgue measure or a finite measure, then the density process has self-intersection local time of order k ≥ 2 if and only if Hd

Keywords: Fractional Brownian motion; fractional Brownian density process; generalized Gaussian process; self-intersection local time; non-semimartingale property (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTP.0000040296.95910.e1

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