Skip to main content
Log in

Monte-Carlo estimation of functionals of solutions of homogeneous integral equations

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

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.

Literature cited

  1. T. Harris, The Theory of Branching Stochastic Processes, Springer, Berlin (1963).

    Google Scholar 

  2. B. A. Sevast'yanov, Branching Processes [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  3. G. Birkhoff, Lattice Theory, AMS, Providence, RI (1948).

    Google Scholar 

  4. G. A. Mikhailov, “Computing critical systems by the Monte-Carlo method,” Zh. Vychislit. Matem. i Matem. Fiz.,6, No. 1, 71–80 (1966).

    Google Scholar 

  5. D. A. Frank-Kamenetskii, “Calculating the multiplication ratio of a nuclear reactor by Monte-Carlo method,” in: Monte-Carlo Method in the Radiation Transfer Problem [in Russian], Atomizdat, Moscow (1967), pp. 212–226.

    Google Scholar 

  6. J. A. Lieberoth, “A Monte-Carlo technique to solve the static eigenvalue problem of the Boltzmann transport equation,” Nukleonik,11, No. 5, 213–219 (1968).

    Google Scholar 

  7. B. A. Sevast'yanov and A. M. Zubkov, “Controlled branching processes,” Teor. Veroyatn. Ee Primen.,19, No. 2, 319–339 (1974).

    Google Scholar 

  8. R. Kh. Khairullin, On Some Connections Between Markov Processes and the Theory of Positive Operators [in Russian], Abstract of Thesis, Kazan' (1972).

  9. R. Kh. Khairullin, “On a Monte-Carlo algorithm for computing critical systems,” Izv. Vuzov, Matem., No. 10, 138–149 (1977).

    Google Scholar 

  10. R. Kh. Khairullin, “On estimating the critical parameter for one class of branching processes,” Izv. Vuzov, Matem., No. 8, 77–84 (1980).

    Google Scholar 

  11. V. G. Zolotukhin and L. V. Maiorov, Estimation of Parameter Criticality Parameters by Monte-Carlo Method [in Russian], Energoatomizdat, Moscow (1984).

    Google Scholar 

  12. S. M. Ermakov and A. A. Zhiglyavskii, “The Monte-Carlo method for estimation of functionals of eigenmeasures of linear integral operators,” Zh. Vychislit. Matem. i Matem. Fiz.,25, No. 5, 666–679 (1985).

    Google Scholar 

  13. V. S. Vladimirov, “On application of the Monte-Carlo method to find the least characteristic value and the corresponding eigenfunction of a linear integral equation,” Teor. Veroyatn. Ee Primen.,1, No. 1, 113–130 (1956).

    Google Scholar 

  14. J. L. Doob, Stochastic Processes [Russian translation], IL, Moscow (1956).

    Google Scholar 

Download references

Authors

Additional information

Translated from Issledovaniya po Prikladnoi Matematike, Kazan', No. 14, pp. 144–159, 1987.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khairullin, R.K. Monte-Carlo estimation of functionals of solutions of homogeneous integral equations. J Math Sci 50, 1884–1894 (1990). https://doi.org/10.1007/BF01097212

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01097212

Keywords

Navigation