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Fields with Exceptional Tangent Fields

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  • Céline Lacaux

    (Université Paul Sabatier UFR MIG)

Abstract

The asymptotic self-similarity property describes the local structure of a random field. In this paper, we introduce a locally asymptotically self-similar second order field XH,β whose local structures at x=0 and at x≠0 are very far from each other. More precisely, whereas its tangent field at x≠0 is a Fractional Brownian Motion, its tangent field at x=0 is a Fractional Stable Motion. In addition, XH,β is asymptotically self-similar at infinity with a Gaussian field, which is not a Fractional Brownian Motion, as tangent field. Then, its trajectories regularity is studied. Finally, the Hausdorff dimension of its graphs is given.

Suggested Citation

  • Céline Lacaux, 2005. "Fields with Exceptional Tangent Fields," Journal of Theoretical Probability, Springer, vol. 18(2), pages 481-497, April.
    • Handle: RePEc:spr:jotpro:v:18:y:2005:i:2:d:10.1007_s10959-005-3516-7
    DOI: 10.1007/s10959-005-3516-7
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    References listed on IDEAS

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    1. Albert Benassi & Pierre Bertrand & Serge Cohen & Jacques Istas, 2000. "Identification of the Hurst Index of a Step Fractional Brownian Motion," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 101-111, January.
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