Abstract
For a sequence of random iterations, we study the set of partial limits and the frequency of visiting their neighborhoods.
Similar content being viewed by others
References
T. Morozan, “Periodic solutions of stochastic discrete systems,”Rev. Roum. Math. Pures. Appl.,32, No. 4, 351–363 (1987).
A. Ya. Dorogovtsev,Periodic and Stationary Modes of Infinite-Dimensional Deterministic and Stochastic Systems [in Russian] Vyshcha Shkola, Kiev 1992.
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.
A. A. Dorogovtsev, “On the convergence of iterations disturbed by strong Gaussian random operator,”Stochastics Stochast. Repts.,43, 117–126 (1993).
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.
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.
L. Kuipers and H. Niederreiter,Uniform Distribution of Sequences, Wiley, New York 1974.
V. V. Petrov,Limit Theorems for Sums of Independent Random Variables [in Russian] Nauka, Moscow 1987.
P. Billingsley,Convergence of Probability Measures, Wiley, New York 1968.
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).
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02383865