Skip to main content
Log in

Some characteristics of sequences of iterations with random perturbations

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For a sequence of random iterations, we study the set of partial limits and the frequency of visiting their neighborhoods.

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. T. Morozan, “Periodic solutions of stochastic discrete systems,”Rev. Roum. Math. Pures. Appl.,32, No. 4, 351–363 (1987).

    MATH  MathSciNet  Google Scholar 

  2. A. Ya. Dorogovtsev,Periodic and Stationary Modes of Infinite-Dimensional Deterministic and Stochastic Systems [in Russian] Vyshcha Shkola, Kiev 1992.

    Google Scholar 

  3. A. Ya. Dorogovtsev and N. A. Denis’evskii, “Convergence of approximations in models with errors,” in:Mathematics Today, 93 [in Russian], Vyshcha Shkola, Kiev (1993), pp. 40–53.

    Google Scholar 

  4. A. A. Dorogovtsev, “On the convergence of iterations disturbed by strong Gaussian random operator,”Stochastics Stochast. Repts.,43, 117–126 (1993).

    MATH  MathSciNet  Google Scholar 

  5. A. M. Kulik, “Trajectorywise limit behavior of sequences of random variables,” in:Random Processes and Infinite-Dimensional Analysis [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 75–87.

    Google Scholar 

  6. A. A. Dorogovtsev and N. A. Denis’evskii, “Iteration approaches to the solution of the Cauchy problem with random noise,” in:Nonlinear Boundary-Value Problems in Mathematical Physics and Their Applications. Abstracts [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1994), p. 71.

    Google Scholar 

  7. L. Kuipers and H. Niederreiter,Uniform Distribution of Sequences, Wiley, New York 1974.

    MATH  Google Scholar 

  8. V. V. Petrov,Limit Theorems for Sums of Independent Random Variables [in Russian] Nauka, Moscow 1987.

    MATH  Google Scholar 

  9. P. Billingsley,Convergence of Probability Measures, Wiley, New York 1968.

    MATH  Google Scholar 

  10. V. V. Buldygin and S. A. Solntsev, “Contraction principle and strong law of large numbers for weighted sums,”Teor. Ver. Prim.,31, No. 3, 516–529 (1986).

    MathSciNet  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dorogovtsev, A.A. Some characteristics of sequences of iterations with random perturbations. Ukr Math J 48, 1182–1201 (1996). https://doi.org/10.1007/BF02383865

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02383865

Keywords

Navigation