Visitation measures for non-linear iterations with random perturbations

Анотація

A sequence of non-linear iterations with non-identically distributed random perturbations is studied. The asymptotic behaviour of the sequence is described via its visitations measures, which are deterministic measures that allow one to estimate the time spent by the sequence in the neighbourhoods of its partial limits. The results obtained are compared with statements regarding the statistical convergence of the sequence of iterations under study.

Біографії авторів

A. A. Dorogovtsev, Institute of Mathematics of the National Academy of Sciences of Ukraine Kyiv, Ukraine

Institute of Mathematics of the National Academy of Sciences of Ukraine
Kyiv, Ukraine

I. I. Nishchenko, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” Kyiv, Ukraine

National Technical University of Ukraine
“Igor Sikorsky Kyiv Polytechnic Institute”
Kyiv, Ukraine

Посилання

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

A.A. Dorogovtsev, Visiting measures and an ergodic theorem for a sequence of iterations with random perturbations, Ukr. Math. J. 51 (1999), 134–139. https://doi.org/10.1007/BF02591922

H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.

H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74.

M.A. Vlasenko, Local visitation measures for some sequences of random variables with decreasing coefficients, Theory Probab. Appl. 49 (1) (2005), 176–186. https://doi.org/10.1137/S0040585X97980919 https://api.semanticscholar.org/CorpusID:123288655

Опубліковано
2026-09-22
Як цитувати
Dorogovtsev, A. A., & Nishchenko, I. I. (2026). Visitation measures for non-linear iterations with random perturbations. Математичні студії, 66(1), 105-112. https://doi.org/10.30970/ms.66.1.105-112
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