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Dimension properties of sample paths of self-similar processes

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Abstract

The Hausdorff dimensions of the image and the graph of random fields are given under general conditions. The results can be used to a wider class of self-similar random fields and processes, including Brownian motion, Brownian sheet, fractional Brownian motion, processes with stable or (α, β)-fractional stable components.

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Authors and Affiliations

  1. Department of Mathematics, Wuhan University, 430072, Wuhan, China

    Xiao Yimin

  2. Department of Mathematics, Fujian Normal University, 350007, Fuzhou, China

    Lin Huonan

Authors
  1. Xiao Yimin
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  2. Lin Huonan
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Supported by the National Natural Science Foundation of China

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Yimin, X., Huonan, L. Dimension properties of sample paths of self-similar processes. Acta Mathematica Sinica 10, 289–300 (1994). https://doi.org/10.1007/BF02560719

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  • DOI: https://doi.org/10.1007/BF02560719

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