873 research outputs found
Non-asymptotical sharp exponential estimates for maximum distribution of discontinuous random fields
We offer in this paper the non-asymptotical bilateral sharp exponential
estimates for tail of maximum distribution of {\it discontinuous} random
fields.
Our consideration based on the theory of Prokhorov-Skorokhod spaces of random
fields and on the theory of multivariate Banach spaces of random variables with
exponential decreasing tails of distributions.Comment: arXiv admin note: substantial text overlap with arXiv:1510.0418
Monte-Carlo method for multiple parametric integrals calculation and solving of linear integral Fredholm equations of a second kind, with confidence regions in uniform norm
In this article we offer some modification of Monte-Carlo method for multiple
parametric integral computation and solving of a linear integral Fredholm
equation of a second kind (well posed problem).
We prove that the rate of convergence of offered method is optimal under
natural conditions still in the uniform norm, and construct an asymptotical and
non-asymptotical confidence region, again in the uniform norm
Necessary Conditions for Fractional Hardy-Sobolev's Inequalities
In this short article we obtain some necessary conditions for a so-called
fractional Hardy-Sobolev's inequalities in multidimensional case. We also give
some examples to show the sharpness of these inequalities
Weighted Hardy-Littlewood average operators on bilateral grand Lebesgue spaces
We obtain in this short article the non-asymptotic exact estimations for the
norm of (generalized) weighted Hardy-Littlewood average integral operator in
the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show
the sharpness of these inequalities
Lebesgue-Riesz norm estimates for fractional Laplace transform
We obtain in this short article the bilateral non-asymptotic estimations for
the norm in Lebesgue-Riesz and bilateral Grand Lebesgue spaces of the so-called
fractional Laplace integral transform.
We give also examples to show the sharpness of these inequalities
Non-asymptotic estimation for Bell function, with probabilistic applications
We deduce the non-asymptotical bilateral estimates for moment inequalities
for sums of non-negative independent random variables, based on the
correspondent estimates for the so-called Bell functions and the Poisson
distribution
Weight Hardy-Littlewood Inequalities for Different Powers
In this short article we obtain the non-asymptotic upper and low estimations
for linear and bilinear weight Riesz's functional through the Lebesgue spaces
Central Limit Theorem and exponential tail estimations in mixed (anisotropic) Lebesgue spaces
We study the Central Limit Theorem (CLT) in the so-called mixed (anisotropic)
Lebesgue-Riesz spaces and tail behavior of normed sums of centered random
independent variables (vectors) with values in these spaces
Random processes and Central Limit Theorem in Besov spaces
We study sufficient conditions for the belonging of random process to certain
Besov space and for the Central Limit Theorem (CLT) in these spaces.
We investigate also the non-asymptotic tail behavior of normed sums of
centered random independent variables (vectors) with values in these spaces.
Main apparatus is the theory of mixed (anisotropic) Lebesgue-Riesz spaces, in
particular so-called permutation inequality
Boundedness of Operators in Bilateral Grand Bebesgue Spaces with Exact and Weakly Exact Constant Calculation
In this article we investigate an action of some operators (not necessary to
be linear or sublinear) in the so-called (Bilateral) Grand Lebesgue Spaces
(GLS), in particular, double weight Fourier operators, maximal operators,
imbedding operators etc. We intend to calculate an exact or at least weak exact
values for correspondent imbedding constant. We obtain also interpolation
theorems for GLS spaces.We construct several examples to show the exactness of
offered estimations. In two last sections we introduce anisotropic Grand
Lebesgue Spaces, obtain some estimates for Fourier two-weight inequalities and
calculate Boyd's multidimensional indices for this spaces
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