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Deviation of polynomials from their expectations and isoperimetry
Bernoulli: a journal of mathematical statistics and probability. 2018. Vol. 24. No. 3. P. 2043-2063.
Kosov E., Arutyunyan L.
The article is divided into two parts. In the first part, we study the deviation of a polynomial from its mathematical expectation. This deviation can be estimated from above by Carbery–Wright inequality, so we investigate estimates of the deviation from below. We obtain such type estimates in two different cases: for Gaussian measures and a polynomial of an arbitrary degree and for an arbitrary log-concave measure but only for polynomials of the second degree. In the second part, we deal with the isoperimetric inequality and the Poincaré inequality for probability measures on the real line that are images of the uniform distributions on convex compact sets in R^n under polynomial mappings.
Zelenov G., Theory of Stochastic Processes 2017 Vol. 22 No. 2 P. 79-85
We estimate total variation distances between distributions of polynomials viaL2-norms. ...
Added: November 30, 2019
Bogachev V., Pilipenko A. Y., Shaposhnikov A. V., Journal of Mathematical Analysis and Applications 2014 Vol. 419 No. 2 P. 1023-1044
We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we present a negative solution of the long-standing problem of existence of Sobolev extensions of functions in Gaussian Sobolev spaces from a convex domain to the whole space. ...
Added: January 3, 2015
Remizov I., Modeling and Analysis of Information Systems 2015 Vol. 22 No. 3 P. 337-355
A parabolic partial differential equation 𝑢′𝑡(𝑡, 𝑥) = 𝐿𝑢(𝑡, 𝑥) is considered, where 𝐿 is a linear second-order differential operator with time-independent coefficients, which may depend on 𝑥. We assume that the spatial coordinate 𝑥 belongs to a finite- or infinite-dimensional real separable Hilbert space 𝐻. Assuming the existence of a strongly continuous resolving semigroup ...
Added: October 30, 2018
Bogachev V., Providence : American Mathematical Society, 2010
The book gives a systematic account of the theory of differentiable measures and the Malliavin calculus. ...
Added: March 5, 2014
Kosov E., Journal of Mathematical Analysis and Applications 2018 Vol. 462 No. 1 P. 390-406
We show that a measure on the real line, that is the image of a log-concave measure under a polynomial of degree d, possesses a density from the Nikolskii–Besov class of fractional order 1/d. This result is used to prove an estimate for the total variation distance between such measures in terms of the Fortet–Mourier ...
Added: July 20, 2018
Kolesnikov A., Kosov E., Theory of Stochastic Processes 2017 Vol. 22 No. 38 P. 47-61
Let γ be the standard Gaussian measure on Rn and let Pγ be the space of probability measures that are absolutely continuous with respect to γ. We study lower bounds for the functional Fγ(µ) = Ent(µ) − 1 2W2 2 (µ, ν), where µ ∈ Pγ, ν ∈ Pγ, Ent(µ) = R log µ γ ...
Added: August 21, 2018
Bogachev V., Kolesnikov A., Medvedev K. V., Математический сборник 2005 Т. 196 № 3 С. 3-30
Получено новое тождество для энтропии нелинейного образа меры на Rn, дающее известное неравенство Талаграна. Исследованы треугольные отображения в Rn и R∞, т.е. отображения T, у которых i-я координатная функция T
i зависит только от переменных x 1,…, xi. С помощью этих отображений дано положительное решение известной открытой проблемы о представимости всякой вероятностной меры ν, абсолютно непрерывной ...
Added: March 26, 2013
Kosov E., Fractional Calculus and Applied Analysis 2019 Vol. 22 No. 5 P. 1249-1268
We study fractional smoothness of measures on R^k, that are images of a Gaussian measure under mappings from Gaussian Sobolev classes. As a consequence we obtain Nikolskii--Besov fractional regularity of these distributions under some weak nondegeneracy assumption. ...
Added: December 27, 2019
Bogachev V., Providence : American Mathematical Society, 1998
This book presents a systematic exposition of the modern theory of Gaussian measures. The basic properties of finite and infinite dimensional Gaussian distributions, including their linear and nonlinear transformations, are discussed. The book is intended for graduate students and researchers in probability theory, mathematical statistics, functional analysis, and mathematical physics. It contains a lot of ...
Added: March 10, 2014
Ismagilov R. S., Filippova L., Вестник Московского государственного технического университета им. Н.Э. Баумана. Серия Естественные науки 2017 № 2 С. 12-21
The study examines the problem of approximate integration of multivariable functions. These functions are taken from a space with Gaussian measure. According to it, we calculated the average value of the integral standard deviation from theintegral sum. The paper gives the vanishing order for the standard deviation depending on the parameters that define the integral ...
Added: June 5, 2017
Bogachev V., Malofeev I. I., Potential analysis 2016 Vol. 44 No. 4 P. 767-792
We propose a new construction of surface measures on infinite-dimensional spaces ...
Added: February 1, 2017
Singapore : World Scientific, 2014
A survey of recent progress and open problems in the theory of Gaussian measures is given. ...
Added: January 3, 2015
Bogachev V., Kosov E., Zelenov G., Transactions of the American Mathematical Society 2018 Vol. 370 No. 6 P. 4401-4432
We prove that the distribution density of any non-constant polynomial f(\xi _1,\xi _2,\ldots ) of degree d in independent standard Gaussian random variables \xi _i (possibly, in infinitely many variables) always belongs to the Nikolskii-Besov space B^{1/d}(R) of fractional order 1/d (and this order is best possible), and an analogous result holds for polynomial mappings ...
Added: July 20, 2018
Bogachev V., Kolesnikov A., Теория вероятностей и ее применения 2005 № 50(1) С. 27-51
Показано, что для заданных равномерно выпуклой меры μ на R∞, эквивалентной своему сдвигу на вектор (1,0,0,...), и вероятностной меры ν, абсолютно непрерывной относительно μ, найдется борелевское отображение Т = пространства R∞, переводящее меру μ в v и имеющее вид Т(х) = х + F(x), где F принимает значения в l2. Более того, если мера μ ...
Added: March 23, 2011
Kosov E., Математические заметки 2022 Т. 111 № 1 С. 67-79
In this paper, we study bounds for the total variation distance between distributions of second order polynomials in normal random variables provided that they essentially depend on at least three variables. Moreover, we partially extend some recent bounds for the Kolmogorov distance between the distributions of norms of Gaussian random vectors to the case of ...
Added: June 1, 2022
Bogachev V., Kolesnikov A., / Cornell University. Series math "arxiv.org". 2011. No. 1110.1822.
Given the standard Gaussian measure $\gamma$ on the countable product of lines $\mathbb{R}^{\infty}$ and a probability measure $g \cdot \gamma$ absolutely continuous with respect to $\gamma$, we consider the optimal transportation $T(x) = x + \nabla \varphi(x)$ of $g \cdot \gamma$ to $\gamma$. Assume that the function $|\nabla g|^2/g$ is $\gamma$-integrable. We prove that the ...
Added: March 28, 2013
191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90
It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...
Added: September 23, 2016
Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624
Added: February 27, 2013
Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013
Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...
Added: February 5, 2014
Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70
A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
Added: July 19, 2014
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
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
Added: November 1, 2019
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Sinelshchikov D., Кудряшов Н. А., Theoretical and Mathematical Physics 2018 Vol. 196 No. 2 P. 1230-1240
We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct ...
Added: February 9, 2019