?
Surface measures generated by differentiable measures
Potential analysis. 2016. Vol. 44. No. 4. P. 767-792.
Bogachev V., Malofeev I. I.
We propose a new construction of surface measures on infinite-dimensional spaces
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., 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
Bogachev V., М., Ижевск : , 2016
We present modern theory of weak convergence of measures. ...
Added: February 1, 2017
Ведерников В. А., Semenov P., Общество с ограниченной ответственностью "Образование и Информатика", 2017
In the monography we consider theoretic and methodic origins of fundamental notions in the theory of functions of real variable. The text is designed for future and active school math teachers. ...
Added: March 13, 2018
Bogachev V., Успехи математических наук 2016 Т. 71 № 4 С. 107-154
We give a survey of results about distributions of polynomials on multidimensional spaces with measures. ...
Added: February 1, 2017
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
Shvarts D., / Издательский дом ВШЭ. Серия WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2013. № 9.
We consider measure of the balancedness of the complete signed graph. By definition of this measure it can take values from 0 to 1. But it turns out that its lower bound is strictly greater than 0. This paper presents some evaluations for the minimum measures of balancedness and an algorithm to compute it. The ...
Added: March 2, 2014
De Gruyter, 2017
A survey of the theory of surface measures on infinite-dimensional spaces is given ...
Added: November 1, 2017
Bogachev V., Украинский математический журнал 2020 Vol. 72 No. 9 P. 1159-1178
This paper is a survey of Skorokhod differentiability of measures on linear spaces, which also gives new proofs of some
key results in this area along with some new observations. ...
Added: October 23, 2020
Ulyanov V. V., Теория вероятностей и ее применения 2015 Т. 60 № 2 С. 391-402
В работе рассматриваются различные свойства многочленов от случайных элементов: оценки характеристических функционалов многочленов, стохастическое обобщение теоремы Виноградова о среднем, характеризационная проблема, оценка вероятностей попадания в шары. При этом результаты охватывают случайные элементы со значениями как в конечномерных, так и в бесконечно-мерных гильбертовых пространствах. ...
Added: July 13, 2015
Bogachev V., Springer, 2007
This book gives a systematic presentation of modern measure theory as it has developed over the past century. It includes material for a standard graduate course, advanced material not covered by the standard course but necessary in order to read research literature in the area, and extensive additional information on the most diverse aspects of ...
Added: March 10, 2014
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
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
Singapore : World Scientific, 2014
A survey of recent progress and open problems in the theory of Gaussian measures is given. ...
Added: January 3, 2015
Kosov E., Arutyunyan L., Bernoulli: a journal of mathematical statistics and probability 2018 Vol. 24 No. 3 P. 2043-2063
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 ...
Added: February 2, 2018
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., 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
Malofeev I., Доклады Академии наук 2016 Т. 470 № 1 С. 13-17
В работе получены широкие достаточные условия для существования собственных условных вероятностей, измеримо зависящих от параметра в случае параметрических семейств мер и отображений. ...
Added: June 9, 2020
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
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
Abramovich S., Nikitin Y. Y., Bernoulli News 2017 Vol. 24 No. 1 P. 7-13
The paper describes the rich history of remarkable problem lying at the confluence of number theory and probability. What is the probability of co-prima;lity of two randomly selected random numbers? In russian literature this problem and its solution is attributed to P.L.Chebyshev, but we show that before Chebyshev the solution was given by P. Dirichlet, ...
Added: November 8, 2017
Bogachev V., Kosov E., Popova S., Izvestiya. Mathematics 2021 Vol. 85 No. 5 P. 852-882
New results on distributions of functionals on spaces with Gaussian measures are obtained. ...
Added: October 29, 2021
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