Skip to main content
SpringerLink
Log in

Asymptotic estimates of the mean probability of radiative transfer through an exponentially correlated stochastic medium

  • Published:
Izvestiya, Atmospheric and Oceanic Physics Aims and scope Submit manuscript

Abstract

Various models of exponentially correlated random fields associated with Poisson point ensembles, as well as algorithms for simulating radiative transfer in stochastic media of that type, are considered. Asymptotic estimates for the mean probability of particle (quantum of radiation) passage, assuming that the flow of trajectory intersections with domains of constant random density is Poissonian and using the central limit theorem for the corresponding optical length, are made.

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. P. Switzer, “A Random Set Process in the Plane with a Markovian Property,” Ann. Math. Statist. 36, 1859–1863 (1965).

    Article  Google Scholar 

  2. G. A. Mikhailov, Optimization of Weighted Monte Carlo Methods (Springer, 1992).

  3. G. A. Mikhailov and A. V. Voitishek, Numerical Statistical Modeling. Monte-Karlo Metods: A Tutorial (Akademiya, Moscow, 2006) [in Russian].

    Google Scholar 

  4. G. A. Mikhailov and T. A. Averina, “Statistical Modeling of Inhomogeneous Random Functions on the Basis of Poisson Point Fields,” Dokl. Math. 82(2), 701–704 (2010).

    Article  Google Scholar 

  5. S. M. Prigarin, Numerical Modeling Methods for Random Processes and Fields (Inst. Comput. Math. Geophys. SB RAS, Novosibirsk, 2005) [in Russian].

    Google Scholar 

  6. A. Yu. Ambos and G. A. Mikhailov, “Statistical Modelling of the Exponentially Correlated Multivariate Random Field,” Russ. J. Numer. Anal. Math. Modell. 26(3), 213–232 (2011).

    Google Scholar 

  7. J. Serra, Image Analysis and Mathematical Morphology (Academic Press, London, 1982).

    Google Scholar 

  8. W. Veller, An Introduction to Probability Theory and Its Applications Vol. 2 (Wiley, 1966; Mir, Moscow, 1967).

  9. G. A. Mikhailov, “Asymptotics of the Average Radiation Intensity for Some Models of Stochastic Media,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 18(2), 1289–1295 (1982).

    Google Scholar 

  10. I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Dependent Variables (Nauka, Moscow, 1965) [in Russian].

    Google Scholar 

  11. G. A. Mikhailov and A. S. Serednyakov, “Numerical and Asymptotic Estimates for the Influence of the Dimension of the Stochastic Medium Model on Radiative Transfer Estimates,” Opt. Atmos. Okeana 10(3), 201–210 (1997).

    Google Scholar 

  12. B. Davison, Neutron Transport Theory (Clarendon, Oxford, 1958; Atomizdat, Moscow, 1960).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 6, Novosibirsk, 630090, Russia

    G. A. Mikhailov

Authors
  1. G. A. Mikhailov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. A. Mikhailov.

Additional information

Original Russian Text © G.A. Mikhailov, 2012, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2012, Vol. 48, No. 6, pp. 691–697.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mikhailov, G.A. Asymptotic estimates of the mean probability of radiative transfer through an exponentially correlated stochastic medium. Izv. Atmos. Ocean. Phys. 48, 618–624 (2012). https://doi.org/10.1134/S0001433812060084

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001433812060084

Keywords

Search

Navigation