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The functional iterated logarithm law for stochastic processes represented by multiple Wiener integrals
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  • Published: September 1987

The functional iterated logarithm law for stochastic processes represented by multiple Wiener integrals

  • Toshio Mori1 &
  • Hiroshi Oodaira2 

Probability Theory and Related Fields volume 76, pages 299–310 (1987)Cite this article

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  • 6 Citations

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Summary

In a previous paper the authors obtained a functional law of the iterated logarithm for a class of self-similar processes\(\bar X\) with stationary increments, which are represented by multiple Wiener integrals. This result is extended to a certain class of processes represented by multiple Wiener integrals which converge to\(\bar X\) with an appropriate normalization. As an application a functional log log law for nonlinear functionals of some stationary Gaussian processes is given.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Yokohama City University, 22-2 Seto, Kanazawa-ku, 236, Yokohama, Japan

    Toshio Mori

  2. Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Tokiwadai, Hodogaya-ku, 240, Yokohama, Japan

    Hiroshi Oodaira

Authors
  1. Toshio Mori
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  2. Hiroshi Oodaira
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Cite this article

Mori, T., Oodaira, H. The functional iterated logarithm law for stochastic processes represented by multiple Wiener integrals. Probab. Th. Rel. Fields 76, 299–310 (1987). https://doi.org/10.1007/BF01297487

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  • Received: 22 October 1985

  • Issue Date: September 1987

  • DOI: https://doi.org/10.1007/BF01297487

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Gaussian Process
  • Iterate Logarithm
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