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pro vyhledávání: '"Berkes, István"'
In this paper we present the theory of lacunary trigonometric sums and lacunary sums of dilated functions, from the origins of the subject up to recent developments. We describe the connections with mathematical topics such as equidistribution and di
Externí odkaz:
http://arxiv.org/abs/2301.05561
Autor:
Berkes, Istvan, Borda, Bence
Publikováno v:
J. Lond. Math. Soc. 108 (2023), 409-440
Random walks on the circle group $\mathbb{R}/\mathbb{Z}$ whose elementary steps are lattice variables with span $\alpha \not\in \mathbb{Q}$ or $p/q \in \mathbb{Q}$ taken mod $\mathbb{Z}$ exhibit delicate behavior. In the rational case we have a rando
Externí odkaz:
http://arxiv.org/abs/2204.00274
Autor:
Berkes, Istvan, Borda, Bence
Publikováno v:
Acta Arithmetica 199 (2021), 303-330
Let $\alpha$ be an irrational number, let $X_1, X_2, \ldots$ be independent, identically distributed, integer-valued random variables, and put $S_k=\sum_{j=1}^k X_j$. Assuming that $X_1$ has finite variance or heavy tails $P (|X_1|>t)\sim ct^{-\beta}
Externí odkaz:
http://arxiv.org/abs/2010.07251
Autor:
Berkes, Istvan, Borda, Bence
Publikováno v:
Acta Arithmetica 191 (2019), 383-415
For irrational $\alpha$, $\{n\alpha\}$ is uniformly distributed mod 1 in the Weyl sense, and the asymptotic behavior of its discrepancy is completely known. In contrast, very few precise results exist for the discrepancy of subsequences $\{n_k \alpha
Externí odkaz:
http://arxiv.org/abs/1910.11766
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Akademický článek
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Autor:
Berkes, István
This paper discusses a forgotten remark of Paul L\'evy (1935), determining the asymptotic distribution of sums of i.i.d. random variables with tails $cx^{-\alpha}\psi(\log x)$, where $0<\alpha<2$ and $\psi$ is a periodic function on $\mathbb R$. Such
Externí odkaz:
http://arxiv.org/abs/1609.08321
We provide exact asymptotics for the tail probabilities $\mathbb{P} \{S_{n,r} > x\}$ as $x \to \infty$, for fix $n$, where $S_{n,r}$ is the $r$-trimmed partial sum of i.i.d. St. Petersburg random variables. In particular, we prove that although the S
Externí odkaz:
http://arxiv.org/abs/1507.02846
Autor:
Berkes, Istvan, Tichy, Robert
By a classical result of Kadec and Pe\l czynski (1962), every normalized weakly null sequence in $L^p$, $p>2$ contains a subsequence equivalent to the unit vector basis of $\ell^2$ or to the unit vector basis of $\ell^p$. In this paper we investigate
Externí odkaz:
http://arxiv.org/abs/1506.07453
We consider the asymptotic normality in $L^2$ of kernel estimators of the long run covariance kernel of stationary functional time series. Our results are established assuming a weakly dependent Bernoulli shift structure for the underlying observatio
Externí odkaz:
http://arxiv.org/abs/1503.00741