Skip to main content
SpringerLink
Log in

Probability distribution of an integral quadratic functional on the trajectories of a complex-valued Ornstein-Uhlenbeck process

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The local limiting theorem for probability distribution density of random values of an additive quadratic functional over the trajectories of the complex-valued Ornstein-Uhlenbeck process is proved. The additive functional support is extended unlimitedly. A guaranteed estimate of the asymptotic formula derived is given.

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. C. W. Helstrom, Quantum Detection and Estimation Theory, Acad. Press, New York (1976).

    Google Scholar 

  2. A. S. Mazmanishvili, “Distribution of intervals to vanishing of the difference of two functions of independent random processes,” Kibernetika, No. 2, 122–127 (1989).

  3. Yu. T. Kostenko and A. S. Mazmanishvili, “Risk and control of a stochastic distributed system using the threshold exceedance probability for an integral quadratic criterion,” Kibernetika, No. 6, 90–95 (1990).

  4. W. K. Pratt, Laser Communication Systems, John Wiley, New York (1970).

    Google Scholar 

  5. A. P. Husu, Yu. R. Vitenberg, and V. A. Pal’mov, Roughness of Surfaces (Probability-Theoretic Approach) [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  6. J. Perina, Quantum Statistics of Linear and Nonlinear Optical Phenomena, Cluwer, Dordrecht (1991).

    Google Scholar 

  7. G. Bedard, “Photon counting statistics in gaussian light,” Phys. Rev., 151, No.4, 1038–1039 (1966).

    Google Scholar 

  8. N. V. Laskin, A. S. Mazmanishvili, N. N. Nasonov, and N. F. Shul’ga, “The Landau-Pomeranchuk effect theory (suppression of the radiation of relativistic electrons in amorphous and crystal media),” ZhETF, 88, No.3(9), 763–780 (1985).

    Google Scholar 

  9. Yu. P. Virchenko, “Percolation mechanism of material ageing and distribution of the destruction time, ” Functional Materials, 5, No.1, 7–13 (1998).

    Google Scholar 

  10. M. Arato, Linear Stochastic Systems with Constant Coefficients. A Statistical Approach, Springer-Verlag, Berlin (1982).

    Google Scholar 

  11. I. I. Gikhman and A. V. Skorokhod, The Theory of Random Processes [in Russian], Vol. 1, Nauka, Moscow (1971).

    Google Scholar 

  12. A. S. Mazmanishvili, Continuum Integration as a Method of Solving Physical Problems [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  13. A. J. F. Siegert, “A systematic approach to a class of problems in the theory of noise and other random phenomena, part II, examples,” in: Trans. IRE, IT-3 (1957), pp. 38–44.

  14. R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev., 131, 2766–2788 (1963).

    Google Scholar 

  15. J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics, Syracuse Univ. Press, New York (1968).

    Google Scholar 

  16. W. Feller, An Introduction to Probability Theory and its Applications, 2nd ed., Vol. 2, John Wiley and Sons. Inc., New York (1972).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Monocrystals, National Academy of Sciences of Ukraine, Kharkov, Ukraine

    Yu. P. Virchenko

  2. National Technical University “Kharkov Polytechnical Institute”, Kharkov, Ukraine

    A. S. Mazmanishvili

Authors
  1. Yu. P. Virchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. Mazmanishvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 130–139, November–December 2004.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Virchenko, Y.P., Mazmanishvili, A.S. Probability distribution of an integral quadratic functional on the trajectories of a complex-valued Ornstein-Uhlenbeck process. Cybern Syst Anal 40, 899–907 (2004). https://doi.org/10.1007/s10559-005-0029-4

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-005-0029-4

Keywords

Search

Navigation