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Information × Registration Number 0223U004855, 0123U102738 , R & D reports Title Asymptotic regimes of perturbed random walks: on the edge of modern and classical probability popup.stage_title Head Iksanov Oleksandr М., Доктор фізико-математичних наук Registration Date 06-12-2023 Organization Taras Shevchenko National University of Kyiv popup.description2  The object of research is iterated globally perturbed random walks on trees of general branching processes, nested employment schemes, random series generated by linear recursions, locally perturbed random walks, self-perturbed random walks, random walks with sticky barriers, inverse random walks on the plane. The subject of research is asymptotics and limit theorems for the listed objects, construction of a skew stable Lévy process and random walks with sticky barriers. The purpose of the work is to build an asymptotic theory of globally and locally perturbed random walks. Results and their novelty. The report presents the results obtained as part of the research work "Asymptotic regimes of perturbed random walks: on the border of modern and classical probability" (2020, 2021, 2023). In these statements, all the main statements of the report are established for the first time. In the first section of the report, the elements of recovery theory for iterated globally perturbed random walks are constructed, which is further used in the second section to analyze nested employment patterns. The third section is devoted to the analysis of discounted random series generated by linear recursions in two formulations. The fourth chapter studies the arithmetic properties of multiplicative perturbed random walks on the set of natural numbers. The fifth chapter lays the foundations of the asymptotic theory of locally perturbed random walks, in particular, random walks with sticky barriers and self-perturbed random walks. In the sixth section, a number of results for inverse random walks on the plane are obtained. Keywords: random walk with a sticky barrier; random wandering with the membrane; nested scheme of employment in a random environment; globally perturbed random walk; discounted random series; generated by linear recursions; locally perturbed random walk; least common multiple; self-inflicted random wandering; recovery theory. Product Description popup.authors Bohdansʹkyy Viktor Yu. Bohun Vladyslav A. Brahanets Oksana А. Kondratenko Oleh О. Kotelʹnykova Valeriya G. Marynych Oleksandr V. Pylypenko Andrii Yu. Raschytov Bogdan S. Samoilenko Igor V. Svatko Ivan Yu. popup.nrat_date 2023-12-06 Close