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Fractional Brownian motion and packing dimension

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Abstract

LetX(t) (tR N) be a fractional Brownian motion of index α inR d. For any compact setER N, we compute the packing dimension ofX(E).

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References

  1. Falconer, K. J. (1990).Fractal Geometry—Mathematical Foundations and Applications. Wiley and Sons.

  2. Kahane, J.-P. (1985).Some Random Series of Functions. 2nd Ed. Cambridge University Press.

  3. Kaufman, R. (1969). Une propriété métrique du mouvement brownien.C. R. Acad. Sci. Paris 268, 727–728.

    Google Scholar 

  4. Monrad, D., and Pitt, L. D. (1986). Local nondeterminism and Hausdorff dimension.Progress in Probability and Statistics. Seminar on Stochastic Processes. Birkhauser, Boston.

    Google Scholar 

  5. Perkins, Ed. A., and Taylor, S. J. (1987). Uniform measure results for the image of subsets under Brownian motion.Prob. Th. Rel. Fields 76, 257–289.

    Google Scholar 

  6. Saint Raymond, X., and Tricot, C. (1988). Packing regularity of sets inn-space.Math. Proc. Camb. Phil. Soc. 103, 133–145.

    Google Scholar 

  7. Taylor, S. J. (1986a). The use of packing measure in the analysis of random sets.Lecture Notes in Math. 1203, 214–222.

    Google Scholar 

  8. Taylor, S. J. (1986b). The measure theory of random fractals.Math. Proc. Camb. Phil. Soc. 100, 383–406.

    Google Scholar 

  9. Tricot, C. (1982). Two definitions of fractional dimension.Math. Proc. Camb. Phil. Soc. 91, 57–74.

    Google Scholar 

  10. Taylor, S. J., and Tricot, C. (1985). Packing measure and its evaluation for a Brownian path.Trans. Amer. Math. Soc. 288, 679–699.

    Google Scholar 

  11. Taylor, S. J., and Tricot, C. (1986). The packing measure of rectifiable subsets of the plane.Math. Proc. Phil. Soc. 99, 285–296.

    Google Scholar 

  12. Xiao, Yimin (1993). Uniform packing dimension results for fractional Brownian motion. InProbability and Statistics—Rencontres Franco-Chinoises en Probabilités et Statistique, (A. Badrikian, P. A. Meyer and J. A. Yan, eds.), pp. 211–219. World Scientific.

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Partially supported by an NSF grant.

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Talagrand, M., Xiao, Y. Fractional Brownian motion and packing dimension. J Theor Probab 9, 579–593 (1996). https://doi.org/10.1007/BF02214076

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  • DOI: https://doi.org/10.1007/BF02214076

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