arXiv subjects

Tengiz Kiria

Publications and source records attributed to Tengiz Kiria.

3 recordsLinked to original sources

arXiv2016

Calculation of Improper Integrals by Using Uniformly Distributed Sequences

We present the proof of a certain modified version of Kolmogorov's strong law of large numbers for calculation of Lebesgue Integrals by using uniformly distributed sequences in $(0,1)$. We extend the result of C. Baxa and J. Schoi$β$engeier (cf.\cite{BaxSch2002}, Theorem 1, p. 271) to a maximal set of uniformly distributed (in $(0,1)$) sequences $S_f \subset(0,1)^{\infty}$ which strictly contains the set of sequences of the form $(\{αn\})_{n \in {\bf N}}$ with irrational number $α$ and for which $\ell_1^{\infty}(S_f)=1$, where $\ell_1^{\infty}$ denotes the infinite power of the linear Lebesgue measure $\ell_1$ in $(0,1)$.

math.CA↗

arXiv2016

Calculation of Lebesgue Integrals by Using Uniformly Distributed Sequences in $(0,1)$

We present modified proof of a certain version of Kolmogorov's strong law of large numbers for calculation of Lebesgue Integrals by using uniformly distributed sequences in $(0,1)$. We extend the result of C. Baxa and J. Schoi$β$engeier (cf.\cite{BaxSch2002}, Theorem 1, p. 271) to a maximal set of uniformly distributed (in $(0,1)$) sequences $S_f \subset(0,1)^{\infty}$ which strictly contains the set of sequences of the form $(\{αn\})_{n \in {\bf N}}$ with irrational number $α$ and for which $\ell_1^{\infty}(S_f)=1$, where $\ell_1^{\infty}$ denotes the infinite power of the linear Lebesgue measure $\ell_1$ in $(0,1)$.

math.FA↗

arXiv2015

On objective and strong objective consistent estimates of unknown parameters for statistical structures in a Polish group admitting an invariant metric

By using the notion of a Haar ambivalent set introduced by Balka, Buczolich and Elekes (2012), essentially new classes of statistical structures having objective and strong objective estimates of unknown parameters are introduced in a Polish non-locally-compact group admitting an invariant metric and relations between them are studied in this paper. An example of such a weakly separated statistical structure is constructed for which a question asking "{\it whether there exists a consistent estimate of an unknown parameter}" is not solvable within the theory $(ZF)~\&~(DC)$. A question asking "{\it whether there exists an objective consistent estimate of an unknown parameter for any statistical structure in a non-locally compact Polish group with an invariant metric when subjective one exists}" is answered positively when there exists at least one such a parameter the pre-image of which under this subjective estimate is a prevalent. These results extend recent results of authors. Some examples of objective and strong objective consistent estimates in a compact Polish group $\{0; 1\}^N$ are considered in this paper.

math.ST↗