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Information × Registration Number 0220U104613, 0120U105521 , R & D reports Title Asymptotic modes of perturbed random walks: on the border of modern and classical probability theory. popup.stage_title Head Iksanov Oleksandr M., Доктор фізико-математичних наук Registration Date 23-12-2020 Organization Taras Shevchenko National University of Kyiv popup.description2  The results obtained in the framework of the first stage of research work "Asymptotic modes of perturbed random walks: on the verge of modern and classical probability" are presented. In particular, we have constructed elements of the recovery theory for iterated globally perturbed random walks in the intermediate levels of trees of general branching processes. In the first section, we formulate and prove analogs of a number of classical theorems of the theory of recovery for intermediate levels of iterated globally perturbed random walks, namely, analogues of the elementary recovery theorem, Blackwell's theorem, the key recovery theorem, and for strengthening the tree. Several uniform as well as asymptotic estimates for the analog of the function of recovery of iterated globally perturbed random walks have been established. A multidimensional central limit theorem is proved for analogs of the recovery process in intermediate levels of iterated globally perturbed random walks. In the second section, the constructed theory is applied to the intermediate levels of nested employment schemes in random environments generated by the process of stick breaking. Product Description popup.authors Bogun Vladyslav A. Kotelʹnykova Valeriya G. Marynych Оleksandr V. Raschytov Bogdan S. Samoilenko Igor V. Svatko Ivan Yu. popup.nrat_date 2020-12-23 Close