Skip to main content
SpringerLink
Log in

Integral quadratic functionals defined in a normal Markov two-dimensional field and their statistics

  • Published:
Radiophysics and Quantum Electronics Aims and scope

Abstract

We consider the problem of distribution of an integral quadratic functional defined in a stationary two-dimensional random normal Markov field. The generating function of the random-value probability distribution of the functional is found and an approximate expression for the probability distribution is obtained. The effect of the parameters of the two-dimensional field on the statistical properties of the distribution of the considered functional is analyzed. A generalization of the solution to the case of a multidimensional stationary normal Markov field is proposed.

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

References

  1. S. M. Rytov,Introduction to Statistical Radiophysics [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  2. A. Habidi,Proc. IEEE,60, No. 7, 878 (1972).

    Article  Google Scholar 

  3. K. K. Vasil’yev and V. A. Omel’chenko eds.,Applied Theory of Random Processes and Fields [in Russian], Ul’yanovsk State Technical University Press, Ul’Yanovsk (1995).

    Google Scholar 

  4. I. M. Koval’chik and L. A. Yanovich,Generalized Wiener Integral and Its Applications [in Russian], Nauka i Tekhnika, Minsk (1989).

    MATH  Google Scholar 

  5. A. V. Korennoy and S. A. Egorov,Radiotekhnika, No. 1, 43 (1998).

    Google Scholar 

  6. V. I. Tikhonov and M. A. Mironov,Markov Processes [in Russian], Sovetskoye Radio, Moscow (1977).

    MATH  Google Scholar 

  7. C. W. Helstrom,Quantum Detection and Estimation Theory [Russian translation], Mir, Moscow (1979).

    Google Scholar 

  8. A. S. Mazmanishvili,Functional Integration as a Method for Solving Physical Problems [in Russian], Naukova Dumka, Kiev (1987)

    Google Scholar 

  9. A. N. Malakhov,Cumulant Analysis of Random Non-Gaussian Processes and Their Transformations [in Russian], Sovetskoye Radio, Moscow (1978).

    Google Scholar 

  10. Yu. P. Virchenko and A. S. Mazmanishvili,Izv. Vyssh. Uchebn. Zaved., Radiofiz.,39, No. 7, 916 (1996).

    Google Scholar 

  11. N. V. Laskin, N. N. Nasonov, A. S. Mazmanishvili, and N. F. Shul’ga,Zh. Éksp. Teor. Fiz.,88, No. 3, 763 (1985).

    ADS  Google Scholar 

  12. Yu. P. Virchenko, Yu. T. Kostenko, and A. S. Mazmanishvili,Probabilistic Models of Random Processes and Functionals in Applied Problems [in Russian], UMK VO Press, Kiev (1992).

    Google Scholar 

  13. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi,Higher Transcendental Functions (Bateman Manuscript Project), Vol. I, McGraw-Hill New York, N.Y. (1953).

    Google Scholar 

  14. A. A. Galuza and A. S. Mazmanishvili, in:Proc. Int. Conf. “Mathematical Methods in Electromagmetic Theory (MMET-98),” Kharkov (1998), p. 429.

Download references

Authors
  1. A. S. Mazmanishvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Kharkov State Polytechnical University, Kharkov, Ukraine Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 6, pp. 562–572, June, 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mazmanishvili, A.S. Integral quadratic functionals defined in a normal Markov two-dimensional field and their statistics. Radiophys Quantum Electron 43, 508–517 (2000). https://doi.org/10.1007/BF02677179

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02677179

Keywords

Search

Navigation