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Bivariate occupation measure dimension of multidimensional processes

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  • Bardet, Jean-Marc

Abstract

Bivariate occupation measure dimension is a new dimension for multidimensional random processes. This dimension is given by the asymptotic behavior of its bivariate occupation measure. Firstly, we compare this dimension with the Hausdorff dimension. Secondly, we study relations between these dimensions and the existence of local time or self-intersection local time of the process. Finally, we compute the local correlation dimension of multidimensional Gaussian and stable processes with local Hölder properties and show it has the same value that the Hausdorff dimension of its image have. By the way, we give a new a.s. convergence of the bivariate occupation measure of a multidimensional fractional Brownian or particular stable motion (and thus of a spatial Brownian or Lévy stable motion).

Suggested Citation

  • Bardet, Jean-Marc, 2002. "Bivariate occupation measure dimension of multidimensional processes," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 323-348, June.
    • Handle: RePEc:eee:spapps:v:99:y:2002:i:2:p:323-348
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    References listed on IDEAS

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    1. Rosen, Jay, 1987. "The intersection local time of fractional Brownian motion in the plane," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 37-46, October.
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    Cited by:

    1. Dhifaoui, Zouhaier & Bardet, Jean-Marc, 2022. "Local correlation dimension of multidimensional stochastic process," Statistics & Probability Letters, Elsevier, vol. 181(C).

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