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L. Sirota

Publications and source records attributed to L. Sirota.

At least 19 recordsLinked to original sources
arXiv2024

Exact exponential tail estimation for sums of independent centered random variables, under natural norming, with applications to the theory of U-statistics

We derive in this short report the exact exponential decreasing tail of distribution for naturel normed sums of independent centered random variables (r.v.), applying the theory of Grand Lebesgue Spaces (GLS). We consider also some applications into the theory of U statistics, where we deduce alike for the independent variables the refined exponential tail estimates for ones under natural norming sequence.

math.PR↗
arXiv2024

Ordinary and logarithmical convexity of moment generating function

We establish an ordinary as well as a logarithmical convexity of the Moment Generating Function (MGF) for the centered random variable and vector (r.v.) satisfying the Kramer's condition. Our considerations are based on the theory of the so-called Grand Lebesgue Spaces.

math.PR↗
arXiv2022

Generalized Grand Lebesgue Spaces norm estimations for some operators

We study moment rearrangement invariant spaces, which contain as particular cases the generalized Grand Lebesgue Spaces, and provide norm estimates for some operators, not necessarily linear, acting between some measurable rearrangement invariant spaces. The estimations are formulated in the terms of fundamental functions for these spaces.

math.FA↗
arXiv2022

Covariation inequality in Grand Lebesgue Spaces

We represent in this preprint the exact estimate for covariation berween two random variables (r.v.), which are measurable relative the corresponding sigma-algebras through anyhow mixing coefficients. We associate a solution of this problem with fundamental function for correspondent rearrangement invariant spaces.

math.PR↗
arXiv2022

Averaging of random variables and fields

We will prove that by averaging of random variables (r.v.) and random fields (r.f.) its tails of distributions do not increase in comparison with the tails of source variables, essentially or almost exact, under very weak conditions.

math.PR↗
arXiv2022

Generalization of tail inequalities for random variables, using in the martingale theory

We generalize a famous tail Doob's inequality, relative two non-negative random variables, arising in the martingale theory, in two directions: on the more general source data and on the random variables belonging to the so-called Grand Lebesgue Spaces. We bring also several examples in each sections in order to show the exactness of our estimates.

math.PR↗
arXiv2021

Exponential confidence region based on the projection density estimate. Recursivity of these estimations

We investigate the famous Tchentzov's projection density statistical estimation in order to deduce the exponential decreasing tail of distribution for the natural normalized deviation. We modify these estimations assuming the square integrability of estimated function, to make it recursive form, which is more convenient for applications, however they have at the same speed of convergence as the for the classical ones in the composite Hilbert space norm.

math.ST↗
arXiv2021

Generalization and refinement of Khintchin's inequality

We derive the exponential as well as power decreasing tail estimations for normed sums of centered independent identical distributed (or not) random variables on the Khintchine's form. We consider arbitrary, in particular, non-Rademacher's variables and not only Lebesgue-Riesz rearrangement invariant norms for the random variables. We intend to calculate the value of correspondent limit.

math.PR↗