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Sojourns of Multidimensional Gaussian Processes

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Dependence in Probability and Statistics

Part of the book series: Progress in Probability and Statistics ((PRPR,volume 11))

Abstract

We shall survey some recent results on sojourns of multidimensional stationary Gaussian processes with strongly dependent structures, given by Berman [2], Maejima [6],[7] and Taqqu [9].

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Reference

  1. Berman, S.M. (1979): High level sojourns for strongly dependent Gaussian processes. Z. Wahrsch. 50, 223–239.

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  2. Berman, S.M. (1984): Sojourns of vector Gaussian processes inside and outside spheres. Z. Wahrsch. 66, 529–542.

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  3. Dobrushin, R.L. and Major, P. (1979): Non-central limit theorems for non-linear functionals of Gaussian fields. Z. Wahrsch. 50, 27–52.

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  4. Maejima, M. (1981): Some sojourn time problems for strongly dependent Gaussian processes. Z. Wahrsch. 57, 1–14.

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  5. Maejima, M. (1982): Some limit theorems for sojourn times of strongly dependent Gaussian processes. Z. Wahrsch. 60, 359–380.

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  6. Maejima, M. (1985): Some sojourn time problems for 2-dimensional Gaussian processes. To appear in J. Multivar. Anal.

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  7. Maejima, M. (1985): Sojourns of multidimensional Gaussian processes with dependent components. To appear in Yokohama Math. J.

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  8. Taqqu, M.S. (1979): Convergence of integrated processes of arbitrary Hermite rank. Z. Wahrsch. 50, 53–83.

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  9. Taqqu, M.S. (1984): Sojourn in an elliptical domain. Technical Report No. 630, School of Operations Research and Industrial Engineering, Cornell University.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223, Japan

    Makoto Maejima

Authors
  1. Makoto Maejima
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Editor information

Editors and Affiliations

  1. Institut für Mathematische Stochastik, Universität Freiburg, 7800, Freiburg i. Br., Federal Republic of Germany

    Ernst Eberlein

  2. Department of Mathematics, Boston University, 02215, Boston, MA, USA

    Murad S. Taqqu

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© 1986 Springer Science+Business Media New York

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Maejima, M. (1986). Sojourns of Multidimensional Gaussian Processes. In: Eberlein, E., Taqqu, M.S. (eds) Dependence in Probability and Statistics. Progress in Probability and Statistics, vol 11. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4615-8162-8_4

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  • DOI: https://doi.org/10.1007/978-1-4615-8162-8_4

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4615-8163-5

  • Online ISBN: 978-1-4615-8162-8

  • eBook Packages: Springer Book Archive

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