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PreprintCC BY 4.0arXiv

Visitation measures for non-linear iterations with random perturbations

  • Andrey A. Dorogovtsev
  • Iryna Nishchenko
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Abstract

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

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Cite

BibTeXRIS
BibTeX
@misc{dorogovtsev2026visitation,
  title = {{Visitation measures for non-linear iterations with random perturbations}},
  author = {Andrey A. Dorogovtsev and Iryna Nishchenko},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37846},
  eprint = {2609.37846},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37846},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Visitation measures for non-linear iterations with random perturbations
AU  - Andrey A. Dorogovtsev
AU  - Iryna Nishchenko
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37846
UR  - https://arxiv.org/abs/2609.37846
AB  - 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
ER  -