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

Author

Listed:
  • T. Bojdecki

    (University of Warsaw)

  • L. G. Gorostiza

    (Centro de Investigación y de Estudios Avanzados)

  • A. Talarczyk

    (University of Warsaw)

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

Suggested Citation

  • T. Bojdecki & L. G. Gorostiza & A. Talarczyk, 2004. "Fractional Brownian Density Process and Its Self-Intersection Local Time of Order k," Journal of Theoretical Probability, Springer, vol. 17(3), pages 717-739, July.
    • Handle: RePEc:spr:jotpro:v:17:y:2004:i:3:d:10.1023_b:jotp.0000040296.95910.e1
    DOI: 10.1023/B:JOTP.0000040296.95910.e1
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    References listed on IDEAS

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    1. Talarczyk, Anna, 2001. "Self-intersection local time of order k for Gaussian processes in," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 17-72, November.
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    Cited by:

    1. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2015. "From intersection local time to the Rosenblatt process," Journal of Theoretical Probability, Springer, vol. 28(3), pages 1227-1249, September.

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