Fields with Exceptional Tangent Fields

Céline Lacaux ()
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Céline Lacaux: Université Paul Sabatier UFR MIG

Journal of Theoretical Probability, 2005, vol. 18, issue 2, 481-497

Abstract: 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.

Keywords: Local asymptotic self-similarity; tangent fields; infinitely divisible distributions (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10959-005-3516-7

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