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Bayesian Disorder Problems on Filtered Probability Spaces
Theory of Probability and Its Applications. 2013. Vol. 57. No. 3. P. 497-511.
Zhitlukhin M., Shiryaev A.
Translator: Zhitlukhin M., A. Shiryaev
We formulate a general Bayesian disorder detection problem, which generalizes models considered in the literature. We study properties of basic statistics, which allow us to reduce problems of quickest detection of disorder moments to optimal stopping problems. Using general results, we consider in detail a disorder problem for Brownian motion on a finite time segment.
Tamm M., Majumdar S., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2012 Vol. 86 P. 021135
We compute analytically the mean number of common sites, WN(t), visited by N independent random walkers each of length t and all starting at the origin at t=0 in d dimensions. We show that in the (N−d) plane, there are three distinct regimes for the asymptotic large-t growth of WN(t). These three regimes are separated by two critical lines d=2 and d=dc(N)=2N/(N−1) in the (N-d) plane. For d<2, WN(t)∼td/2 for large t (the N dependence is ...
Added: November 18, 2013
Tamm M., Stadnichuk V., Ilyina A. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2014 Vol. 89 P. 042137
We consider two random walkers starting at the same time t = 0 from different points in space separated by a given distance R. We compute the average volume of the space visited by both walkers up to time t as a function of R and t and dimensionality of space d. For d < 4, this volume, after proper renormalization, is shown to be ...
Added: May 23, 2014
Zhitlukhin M., Муравлев А. А., Shiryaev A., Russian Mathematical Surveys 2013 Vol. 68 No. 2 P. 389-394
We find the exact optimal decision rule in the problem of testing two hypotheses about the drift of a Brownian motion in the setting of Kiefer and Weiss. ...
Added: March 9, 2014
A. A, Gushchin, Urusov M. A., Russian Mathematical Surveys 2019 Vol. 74 No. 5 P. 953-955
We prove that a right-continuous integrable stochastic process admits a minimal embedding in the standard Brownian motion if and only if it is a submartingale or supermartingale. ...
Added: July 20, 2020
Zhitlukhin M., Alexey Muravlev, Theory of Probability and Its Applications 2013 Vol. 57 No. 4 P. 708-717
This paper contains detailed exposition of the results presented in the short communication [M. V. Zhitlukhin and A. A. Muravlev, Russian Math. Surveys, 66 (2011), pp. 1012–1013]. We consider Chernoff’s problem of sequential testing of two hypotheses about the sign of the drift of a Brownian motion under the assumption that it is normally distributed. ...
Added: February 12, 2014
Pusev R. S., Theory of Probability and Its Applications 2013 Vol. 57 No. 1 P. 60-81
We find precise small deviation asymptotics for some Brownian functionals in the weighted Hilbert norm without knowing of eigenfunctions of corresponding integral Fredholm operators. As particular cases we find for the first time the small deviation asymptotics of Brownian excursion and Brownian meander. ...
Added: January 30, 2015
Decrouez G. G., Jones O. D., The Annals of Applied Probability 2012 Vol. 22 No. 6 P. 2357-2387
We present a new class of multifractal process on R, constructed using an embedded branching process. The construction makes use of known results on multitype branching random walks, and along the way constructs cascade measures on the boundaries of multitype Galton–Watson trees. Our class of processes includes Brownian motion subjected to a continuous multifractal time-change. In ...
Added: September 29, 2014
Nikitin Ya. Yu., Pusev R. S., Theory of Probability and Its Applications 2013 Vol. 57 No. 1 P. 60-81
We find exact small deviation asymptotics with respect to weighted Hilbert norm for some well-known Gaussian processes. Our approach does not assume the knowledge of eigenfunctions of the correspondinge covariance operator. This makes it possible to generalize many previous results in this area. We also obtain ultimate results connected with exact small deviation of Brownian ...
Added: February 28, 2015
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
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
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
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
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
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
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2021.
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold ...
Added: April 7, 2022
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Arzhantsev I., Journal of Lie Theory 2000 Vol. 10 No. 2 P. 345-357
Added: July 8, 2014
Кокоулина М. В., Епифанова А. С., Pelinovsky E. et al., Труды НГТУ им. Р.Е. Алексеева 2020 № 3 С. 28-41
Purpose: to analyze the dynamics of COVID-19 development using a generalized stochastic logistic equation to esti-mate the number of probable peaks in coronavirus incidence and to evaluate the nature of the scatter of the generalized logistic model coefficients.
Design/methodology/approach: we use a logistic model based on a generalized first-order logistic equation. The data on the incidence ...
Added: September 29, 2020
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016
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
Семин С. В., Kurkina O. E., Kurkin A. A. et al., Труды НГТУ им. Р.Е. Алексеева 2012 № 2(95) С. 48-65
Purpose: Numerical modeling of internal baroclinic disturbances of different shapes in a model lake with variable depth, analysis of velocity field of wave-induced current, especially in the near-bed layer.
Approach: The study is carried out with the use of numerical full nonlinear nonhydrostatic model for stratified fluid.
Findings: The full nonlinear numerical modeling of internal wave dynamics ...
Added: October 6, 2012