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On bilinear forms in Gaussian random variables and Toeplitz matrices
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  • Published: September 1988

On bilinear forms in Gaussian random variables and Toeplitz matrices

  • F. Avram1 

Probability Theory and Related Fields volume 79, pages 37–45 (1988)Cite this article

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Summary

We improve a result of Szegő on the asymptotic behaviour of the trace of products of Toeplitz matrices.

As an application, we improve also his results on the limiting behaviour of the bilinear forms

$$B_n = \sum\limits_{i,j = 1}^n {a_{i - j} X_i X_{j,} } $$

where X iis a stationary Gaussian sequence.

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Author information

Authors and Affiliations

  1. Mathematics Department, Northeastern University, 02114, Boston, MA, USA

    F. Avram

Authors
  1. F. Avram
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Additional information

This research was partially supported by the Air Force Office of Scientific Research Contract No. F49620 85C 0144 and partially supported by the Army Research Office through the Mathematical Sciences Institute of Cornell University

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Cite this article

Avram, F. On bilinear forms in Gaussian random variables and Toeplitz matrices. Probab. Th. Rel. Fields 79, 37–45 (1988). https://doi.org/10.1007/BF00319101

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  • Received: 23 December 1986

  • Revised: 27 November 1987

  • Issue Date: September 1988

  • DOI: https://doi.org/10.1007/BF00319101

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Keywords

  • Stochastic Process
  • Asymptotic Behaviour
  • Probability Theory
  • Statistical Theory
  • Bilinear Form
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