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Further Developments in Fractals and Related Fields pp 255–288Cite as

Birkhäuser

Recent Developments on Fractal Properties of Gaussian Random Fields

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Abstract

We review some recent developments in studying fractal and analytic properties of Gaussian random fields. It is shown that various forms of strong local nondeterminism are useful for studying many fine properties of Gaussian random fields. A list of open questions is included.

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Acknowledgements

The author thanks the referee for his/her helpful comments which have led to improvement of the manuscript. Research partially supported by the NSF grant DMS-1006903.

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  1. Department of Statistics and Probability, Michigan State University, A-413 Wells Hall, East Lansing, MI, 48824, USA

    Yimin Xiao

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  1. , LAGA, Université Paris 13, avenue J.B. Clément 99, Villetaneuse, 93430, France

    Julien Barral

  2. , Laboratoire d'Analyse et de Mathématique, Université Paris-Est Créteil - Val de Ma, Avenue du Général de Gaulle 61, Créteil Cedex, 94010, France

    Stéphane Seuret

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Xiao, Y. (2013). Recent Developments on Fractal Properties of Gaussian Random Fields. In: Barral, J., Seuret, S. (eds) Further Developments in Fractals and Related Fields. Trends in Mathematics. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8400-6_13

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