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Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary
Journal of Functional Analysis. 2012. Vol. 263. P. 248-303.
Borodin A., Olshanski G.
Borodin A., Olshanski G., Advances in Mathematics 2012 Vol. 230 No. 4-6 P. 1738-1779
The Gelfand–Tsetlin graph is an infinite graded graph that encodes branching of irreducible characters of the unitary groups. The boundary of the Gelfand–Tsetlin graph has at least three incarnations — as a discrete potential theory boundary, as the set of finite indecomposable characters of the infinite-dimensional unitary group, and as the set of doubly infinite ...
Added: February 25, 2013
Konakov V., Mammen E., Bernoulli: a journal of mathematical statistics and probability 2005 Vol. 11 No. 4 P. 591-641
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. We prove Edgeworth-type expansions of order o(n-1-δ),δ>0, for transition densities. For this purpose we apply the parametrix method to represent the transition density as a functional of densities of sums of independent and identically distributed variables. Then we apply Edgeworth expansions ...
Added: December 4, 2012
Veretennikov A., Veretennikova M., / Cornell University. Series "Working papers by Cornell University". 2019.
New convergence rate asymptotic bound for a class of homogeneous Markov chains is established. ...
Added: November 14, 2019
Anatoly Manita, Queueing Systems 2014 Vol. 76 No. 2 P. 149-180
We consider a stochastic model of clock synchronization in a wireless network of N sensors interacting with one dedicated accurate time server. For large N we find an estimate of the final time sychronization error for global and relative synchronization. The main results concern the behavior of the network on different timescales tN→∞ , N→∞ ...
Added: February 4, 2015
Piatnitski A., Pirogov S. A., Zhizhina E., Applicable Analysis 2019 Vol. 98 No. 1-2 P. 217-231
The goal of the paper is to describe the large time behaviour of a symmetric diffusion in a high-contrast periodic environment and to characterize the limit process under the diffusive scaling. We consider separately the C_0 and L^2 settings. ...
Added: December 5, 2020
Konakov V., Mammen E., Probability Theory and Related Fields 2000 Vol. 117 No. 4 P. 551-587
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition
densities are proved. ...
Added: October 15, 2012
Kolokoltsov V., Fractional Calculus and Applied Analysis 2019 Vol. 22 No. 3 P. 543-600
This paper aims at unifying and clarifying the recent advances in the analysis of the fractional and generalized fractional Partial Differential Equations of Caputo and Riemann-Liouville type arising essentially from the probabilistic point of view. This point of view leads to the path integral representation for the solutions of these equations, which is seen to ...
Added: November 14, 2019
Konakov V., Mammen E., Probability Theory and Related Fields 2009 Vol. 143 No. 1 P. 137-176
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Second order Edgeworth type expansions for transition densities are proved. The paper differs from recent results in two respects. We allow nonhomogeneous diffusion limits and we treat transition densities with time lag converging to zero. Small time asymptotics are motivated by ...
Added: December 4, 2012
Borodin A., Olshanski G., Moscow Mathematical Journal 2013 Vol. 13 No. 2 P. 191-230
The classification results for the extreme characters of two basic "big" groups, the infinite symmetric group S(infinity) and the infinite-dimensional unitary group U(infinity), are remarkably similar. It does not seem to be possible to explain this phenomenon using a suitable extension of the Schur-Weyl duality to infinite dimension. We suggest an explanation of a different ...
Added: February 25, 2013
Tumanov M., Piunovskly A., Plakhov A., Optimal Control Applications and Methods 2019 P. 1-21
Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the optimality equation. The theory is illustrated by an example from mathematical epidemiology. The developed methods can be also useful for ...
Added: February 27, 2020
Durmus A., Moulines E., Naumov A. et al., / Cornell University. Series arXiv "math". 2023.
In this paper, we establish novel deviation bounds for additive functionals of geometrically ergodic Markov chains similar to Rosenthal and Bernstein-type inequalities for sums of independent random variables. We pay special attention to the dependence of our bounds on the mixing time of the corresponding chain. Our proof technique is, as far as we know, ...
Added: June 18, 2023
Olshanski G., Функциональный анализ и его приложения 2016 Т. 49 № 4 С. 61-75
Ранее А. М. Бородин и автор построили 4-параметрическое семейство марковских процессов на дуальном объекте к бесконечномерной унитарной группе. Основной новый результат состоит в том, что эти процессы являются пределами скачкообразных процессов на дуальных объектах к растущим компактным унитарным группам. ...
Added: December 29, 2016
Kleptsyna M., Veretennikov A., Mathematical Methods of Statistics 2016 Vol. 25 No. 3 P. 207-218
A new result on stability of an optimal nonlinear filter for a Markov chain with respect to small perturbations on every step is established. An exponential recurrence of the signal is assumed. ...
Added: October 16, 2016
Kelbert M., Сухов Ю. М., М. : МЦНМО, 2021
Для освоения теории вероятностей и математической статистики тренировка в решении задач и выработка интуиции важны не меньше, чем
изучение доказательств теорем; большое разнообразие задач по этому предмету затрудняет студентам переход от лекций к экзаменационным задачам,
а от них—к практике. Специфический предмет этого тома, цепи Маркова и их применения,
переживает последнее время большой подъем. Многие замечательные теоретические результаты были ...
Added: February 1, 2021
Olshanski G., / Cornell University. Series math "arxiv.org". 2013. No. 1310.6155.
These are notes for a mini-course of 3 lectures given at the St. Petersburg
School in Probability and Statistical Physics (June 2012). My aim was to
explain, on the example of a particular model, how ideas from the
representation theory of big groups can be applied in probabilistic problems.
The material is based on the joint paper arXiv:1009.2029 by ...
Added: November 16, 2013
Molchanov S., Bogachev L., Derfel G., Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 2015 Vol. 471 P. 1-19
Added: June 22, 2016
Н. Ю. Энатская, Е. Р. Хакимуллин, М. : Юрайт, 2015
Учебник представляет три вероятностных дисциплины: теорию вероятностей, математическую статистику и случайные про-цессы, составляющие основу вероятностного образования студентов. По каждой дисциплине изложены основные теоретичес-кие вопросы и приведены многочисленные примеры и задачи для иллюстрации теории и пояснения ее практического исполь-зования. Кроме решенных задач по всем главам учебника предложены задачи для самостоятельного решения и теоретические вопросы для самоконтроля ...
Added: November 10, 2015
Semin V. G., Качество Инновации Образование, РФ.Москва.Европейский центр по качеству 2014 № 11 С. 61-66
The article presents the results of stochastic modeling of flow of power in a hierarchical structure of the political model of Government - civil society using the apparatus of the equations of Fokker-Planck-Kolmogorov equation. These results are a further development of the well-known mathematical implementation of the General scheme of the system "power-society"that describes the ...
Added: March 14, 2015
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017