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Sojourns of Multidimensional Gaussian Processes

  • Makoto Maejima
Part of the Progress in Probability and Statistics book series (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. [1]
    Berman, S.M. (1979): High level sojourns for strongly dependent Gaussian processes. Z. Wahrsch. 50, 223–239.CrossRefzbMATHGoogle Scholar
  2. [2]
    Berman, S.M. (1984): Sojourns of vector Gaussian processes inside and outside spheres. Z. Wahrsch. 66, 529–542.CrossRefzbMATHGoogle Scholar
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    Dobrushin, R.L. and Major, P. (1979): Non-central limit theorems for non-linear functionals of Gaussian fields. Z. Wahrsch. 50, 27–52.CrossRefzbMATHMathSciNetGoogle Scholar
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    Maejima, M. (1981): Some sojourn time problems for strongly dependent Gaussian processes. Z. Wahrsch. 57, 1–14.CrossRefzbMATHMathSciNetGoogle Scholar
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    Maejima, M. (1982): Some limit theorems for sojourn times of strongly dependent Gaussian processes. Z. Wahrsch. 60, 359–380.CrossRefzbMATHMathSciNetGoogle Scholar
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    Maejima, M. (1985): Some sojourn time problems for 2-dimensional Gaussian processes. To appear in J. Multivar. Anal.Google Scholar
  7. [7]
    Maejima, M. (1985): Sojourns of multidimensional Gaussian processes with dependent components. To appear in Yokohama Math. J.Google Scholar
  8. [8]
    Taqqu, M.S. (1979): Convergence of integrated processes of arbitrary Hermite rank. Z. Wahrsch. 50, 53–83.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [9]
    Taqqu, M.S. (1984): Sojourn in an elliptical domain. Technical Report No. 630, School of Operations Research and Industrial Engineering, Cornell University.Google Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Makoto Maejima
    • 1
  1. 1.Department of MathematicsKeio UniversityKohoku-ku, Yokohama 223Japan

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