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Remarks on limit theorems for nonlinear functionals of Gaussian sequences
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  • Published: May 1987

Remarks on limit theorems for nonlinear functionals of Gaussian sequences

  • Murray Rosenblatt1 

Probability Theory and Related Fields volume 75, pages 1–10 (1987)Cite this article

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Summary

Limit theorems for sums of nonlinear functionals of Gaussian sequences typically obtain as limit distribution that of a single term in an expansion given by Dobrushin [1] for a process subordinate to a Gaussian process. Here we show how one can obtain limit theorems of this type where the limit distribution is that of a full expansion of Dobrushin's type.

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References

  1. Dobrushin, R.L.: Gaussian and their subordinated generalized fields. Ann. Probab. 7, 1–28 (1979)

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  2. Dobrushin, R.L., Major, P.: Non-central limit theorems for nonlinear functionals of Gaussian fields. Z. Wahrscheinlichkeitstheor. Verw. Geb. 50, 27–52 (1979)

    Google Scholar 

  3. Major, P.: Multiple Wiener-Ito integrals. Lect. Notes Math. 849. Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  4. Major, P.: Limit theorems for nonlinear functions of Gaussian sequences Z. Wahrscheinlichkeitstheor. Verw. Geb. 57, 129–158 (1981)

    Google Scholar 

  5. Giraitis, L., Surgailis, D.: CLT and other limit theorems for functionals of Gaussian processes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 70, 191–212 (1985)

    Google Scholar 

  6. Rosenblatt, M.: Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables. Z. Wahrscheinlichkeitstheor. Verw. Geb. 49, 125–132 (1979)

    Google Scholar 

  7. Rosenblatt, M.: Limit theorems for Fourier transforms of functionals of Gaussian sequences. Z. Wahrscheinlichkeitstheor. Verw. Geb. 55, 123–132 (1981)

    Google Scholar 

  8. Taqqu, M.S.: Convergence of iterated processes of arbitrary Hermite rank. Z. Wahrscheinlichkeitstheor. Verw. Geb. 50, 27–52 (1979)

    Google Scholar 

  9. Taqqu, M.S.: Self-similar processes and related ultraviolet and infrared catastrophes. In: Fritz, J., Lebowitz, J., Szasz, D. (eds.) Random fields, vol. II, pp 1057–1096. Amsterdam, New York: North-Holland 1981

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, San Diego, 92093, La Jolla, CA, USA

    Murray Rosenblatt

Authors
  1. Murray Rosenblatt
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Additional information

This research is supported in part by Office of Naval Research contract N00014-81-K-003 and National Science Foundation Grant No. DMS 83-12106

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Cite this article

Rosenblatt, M. Remarks on limit theorems for nonlinear functionals of Gaussian sequences. Probab. Th. Rel. Fields 75, 1–10 (1987). https://doi.org/10.1007/BF00320078

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  • Received: 28 January 1986

  • Revised: 16 July 1986

  • Issue Date: May 1987

  • DOI: https://doi.org/10.1007/BF00320078

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Keywords

  • Stochastic Process
  • Probability Theory
  • Limit Theorem
  • Statistical Theory
  • Gaussian Process
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