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Точная асимптотика малых уклонений в L_2-норме с весом для некоторых гауссовских процессов
Записки научных семинаров ПОМИ РАН. 2009. Т. 364. С. 166-199.
Pusev R., Назаров А. И.
We find the exact small ball asymptotics under weighted L_2-norm for a wide class of Gaussian processes which generate boundary-value problems for ordinary differential equations. Sharp constants in the asymptotics are derived for a number of processes connected with special functions.
Pusev R., Теория вероятностей и ее применения 2010 Т. 55 № 1 С. 187-195
We prove results on an exact small deviation asymptotics in L_2-norm for Matérn processes with arbitrary natural index and on logarithmic asymptotics for Matérn processes and fields with arbitrary indexes. ...
Added: January 28, 2019
Nikitin Y. Y., Pusev R., Теория вероятностей и ее применения 2012 Т. 57 № 1 С. 98-123
We find exact small deviation asymptotics with respect to a weighted Hilbert norm for some well-known Gaussian processes. Our approach does not require knowledge of the eigenfunctions of the covariance operator of a weighted process. Such a peculiarity of the method makes it possible to generalize many previous results in this area. We also obtain ...
Added: January 28, 2019
Pusev R., Теоретическая и математическая физика 2010 Т. 165 № 1 С. 134-144
We obtain results on small deviations of Bogoliubov’s Gaussian measure occurring in the theory of the statistical equilibrium of quantum systems. For some random processes related to Bogoliubov processes, we find the exact asymptotic probability of their small deviations with respect to a Hilbert norm. ...
Added: January 28, 2019
Теоремы сравнения для вероятностей малых уклонений весовых L_2-норм гриновских гауссовских процессов
Pusev R., Назаров А. И., Алгебра и анализ 2013 Т. 25 № 3 С. 131-146
Comparison theorems are proved for small ball probabilities of the Green Gaussian processes in weighted L_2-norms. The sharp small ball asymptotics are found for many classical processes under quite general assumptions on the weight. ...
Added: January 28, 2019
Nikitin Y. Y., Пусев Р. С., Теория вероятностей и ее применения 2012 Т. 57 № 1 С. 98-123
Найдена точная асимптотика малых уклонений в гильбертовой норме ряда процессов, связанных с броуновским движением, в частности, броуновской экскурсии, броуновского меандра и броуновского локального времени. ...
Added: November 26, 2013
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
A. I. Zhdanov., Theory Probability and its Applications 2015 Vol. 60 No. 3 P. 520-527
Let $(X(t),Y(t))$, $t\ge0$, be a zero-mean stationary Gaussian vector process with a covariance functions for components $r_i(t)$ satisfying Pickand's condition $r_i(t)=1-c_i|t|^{\alpha_i}(1+o(1))$, $t\to 0$, $c_i>0$, $0<\alpha_i\le2$, $i=1,2.$ Let $r_i(t)<1$, $i=1,2$, $t>0.$ Assuming that $r\equiv {\bf E}\,X(t)Y(t)\in(-1,1)$ and $\lim_{t,s\rightarrow0}({\bf E}\,X(t)Y(s)-r)/|t-s|^{\min(\alpha_1,\alpha_2)}$ exists, we study the behavior of probability ${\bf P}(\max_{t\in\lbrack0,p]}X(t)Y(t)>u)$ as $u\rightarrow\infty$ for any $p$. In particular, we ...
Added: November 14, 2019
Nazarov A. I., Nikitin Ya. Yu., Mathematics 2018 Vol. 6(4) No. 55 P. 1-9
We study the exact small deviation asymptotics with respect to the Hilbert norm for some mixed Gaussian processes. The simplest example here is the linear combination of the Wiener process and the Brownian bridge. We get the precise final result in this case and in some examples of more complicated processes of similar structure. The ...
Added: May 28, 2018
Zhdanov A., Piterbarg V.I., Extremes 2015 Vol. 18 No. 1 P. 99-108
Let X(t), Y(t), t ≥ 0, be two independent zero-mean stationary Gaussian
processes, whose covariance functions are such that ri (t) = 1 − |t|^{a_{i}} + o(|t|^{a_{i}})
as t → 0, with 0 < a_{i} ≤ 2, i = 1, 2 and both of the functions are less than one
for non-zero t . We derive for any p ...
Added: November 14, 2019
A. I. Zhdanov, V. I. Piterbarg, Theory Probability and its Applications 2018 Vol. 63 No. 1 P. 1-21
Let $\mathbf{\boldsymbol{\xi}}(t)=(\xi_{1}(t),\ldots,\xi_{d}(t))$ be a Gaussian zero mean stationary a.s. continuous vector process. Let $g\colon{\mathbb{R}}^{d}\to {\mathbb{R}}$ be a homogeneous function of positive degree. We study probabilities of high extrema of the Gaussian chaos process $g(\mathbf{\boldsymbol{\xi}}(t))$. Important examples are products of Gaussian processes, $\prod_{i=1}^{d}\xi_{i}(t)$, and quadratic forms $\sum_{i,j=1}^{d}a_{ij}\xi_{i}(t)\xi_{j}(t)$. Methods of our studies include the Laplace saddle point ...
Added: November 14, 2019
Chernyshev V.L., Russian Journal of Mathematical Physics 2016 Vol. 23 No. 3 P. 348-354
On a two-dimensional surface, a Schrödinger operator is considered with a potential whose critical points form a closed curve. We pose the problem of describing the semiclassical spectral series corresponding to this curve. The standard construction for describing the spectral series corresponding to isolated nondegenerate equilibria or to periodic trajectories of Hamiltonian systems is not ...
Added: October 25, 2014
Ya. Yu. Nikitin, Kirichenko A., Central European Journal of Mathematics 2014 Vol. 12 No. 11 P. 1674-1686
We find precise small deviation asymptotics with respect to Hilbert norm for some special Gaussian processes connected to two regression schemes studied by McNeill and hic co-authors. Additionally we obtain precise small deviation asymptotics for the detrended Brownian motion and for the Slepian process. ...
Added: August 26, 2014
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
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
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
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
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
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
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
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