Skip to main content
Log in

Spherical level-crossing measures for chi-square random fields

  • Applied Topics in Control Theory, Mathematical Cybernetics, and Applied Statistics
  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

Spherical measures of exceeding a low level are considered for strongly dependent chi-square fields. The limit distributions are sums of multiple stochastic integrals.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. I. N. Kovalenko and O. V. Sarmanov, A Short Course in the Theory of Stochastic Processes [in Russian], Kiev (1978).

  2. N. N. Leonenko, "On level crossing measures of a Gaussian isotropic field," Teor. Veroyat. Mat. Stat., No. 31, 64–82 (1984).

    Google Scholar 

  3. N. N. Leonenko and A. V. Ivanov, Statistical Analysis of Random Fields [in Russian], Kiev (1986).

  4. N. N. Leonenko and A. Kh. El'-Bassionii, "Limit theorems for some level crossing characteristics," Teor. Veroyat. Mat. Stat., No. 35, 55–60 (1986).

    Google Scholar 

  5. O. V. Sarmanov, "Analysis of stationary Markov processes using eigenfunction expansions," Tr. Mat. Inst. Akad. Nauk SSSR,60, 238–261 (1961).

    Google Scholar 

  6. M. I. Yadrenko, Spectral Theory of Random Fields [in Russian], Kiev (1980).

  7. S. M. Berman, "High level sojourns for strongly dependent Gaussian processes," Z. Wahrsch. verw. Geb.,50, 223–236 (1979).

    Google Scholar 

  8. S. M. Berman, "Sojourns of vector Gaussian processes inside and outside spheres," Z. Wahrsch. verw. Geb.,66, 529–542 (1984).

    Google Scholar 

  9. M. Maejima, "Some sojourn time problems for strongly dependent processes," Z. Wahrsch. verw. Geb.,57, 1–14 (1981).

    Google Scholar 

  10. P. Major, "Multiple Wiener—Ito integrals," Lect. Notes Math., vol. 849 (1981).

Download references

Authors

Additional information

Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 118–128, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leonenko, N.N., Sabirov, S.O. Spherical level-crossing measures for chi-square random fields. J Math Sci 69, 1463–1471 (1994). https://doi.org/10.1007/BF01250593

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01250593

Keywords

Navigation