Skip to main content
SpringerLink
Log in

Random symmetric polynomials

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

Let {Q(n)(x1,...,xn)} be a sequence of symmetric polynomials having a fixed degree equal to k. Let {Xn1,...,Xnn}, n⩾ k, be some sequence of series of random variables (r.v.). We form the sequence of r.v. Yn=Q(n)(Xn1, ... Xnn), n⩾ k One obtains limit theorems for the sequence Yn, under very general assumptions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. B. A. Sevast'yanov, “A class of limit distributions for quadratic forms of normal random variables,” Teor. Veroyatn. Primen.,6, No. 3, 368–372 (1961).

    Google Scholar 

  2. G. G. Gregory, “Large sample theory for U-statistics and tests of fit,” Ann. Statist.,5, No. 1, 110–123 (1977).

    Google Scholar 

  3. A. G. Kurosh, A Course in Higher Algebra [in Russian], GITTL, Moscow (1949).

    Google Scholar 

  4. G. J. Székely, “A limit theorem for elementary symmetric polynomials of independent random variables,” Z. Wahrsch. Verw. Gebiete,59, No. 3, 355–359 (1982).

    Google Scholar 

  5. G. Neuhaus, “Functional limit theorems for U-statistics in the degenerate case,” J. Multivariate Anal.,7, No. 3, 424–439 (1977).

    Google Scholar 

  6. T. L. Malevich and B. A. Abdalimov, “Estimation of the deviation of the distribution of a U-statistic from the normal distribution,” Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 3, 10–13 (1979).

    Google Scholar 

  7. T. F. Mori, “On a Hoeffding-type problem,” Lecture Notes Statist., No. 8, 174–181 (1981).

    Google Scholar 

  8. E. B. Dynkin and A. Mandelbaum, “Symmetric statistics, Poisson point processes, and multiple Wiener integrals,” Ann. Statist.,11, No. 3, 739–745 (1983).

    Google Scholar 

Download references

Authors
  1. V. M. Zolotarev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 170–188, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zolotarev, V.M. Random symmetric polynomials. J Math Sci 38, 2262–2272 (1987). https://doi.org/10.1007/BF01093827

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01093827

Keywords

Search

Navigation