Related papers: Lacunary sequences in analysis, probability and nu…
We study sequences of functions of the form F_p^n -> {0,1} for varying n, and define a notion of convergence based on the induced distributions from restricting the functions to a random affine subspace. Using a decomposition theorem and a…
We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also…
For a difference approximations of multidimensional diffusion, the truncated local limit theorem is proved. Under very mild conditions on the distribution of the difference terms, this theorem provides that the transition probabilities of…
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…
Recently, a new fractional derivative called the conformable fractional derivative is given on based basic limit definition derivative in [4]. Then, the fractional versions of chain rules, exponential functions, Gronwalls inequality,…
The field of analytic combinatorics is dedicated to the creation of effective techniques to study the large-scale behaviour of combinatorial objects. Although classical results in analytic combinatorics are mainly concerned with univariate…
Given a lacunary sequence $(n_k)_{k \in \mathbb{N}}$, arbitrary positive weights $(c_k)_{k \in \mathbb{N}}$ that satisfy a Lindeberg-Feller condition, and a function $f: \mathbb{T} \to \mathbb{R}$ whose Fourier coefficients $\hat{f_k}$…
A general moment bound for sums of products of Gaussian vector's functions extending the moment bound in Taqqu (1977, Lemma 4.5) is established. A general central limit theorem for triangular arrays of nonlinear functionals of…
Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate…
We established the rate of convergence in the central limit theorem for stopped sums of a class of martingale difference sequences.
We estimate the lattice sums arising in the context of the integer point counting in polyhedra.
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
We calculate the triple correlations for the truncated divisor sum $\lambda_{R}(n)$. The $\lambda_{R}(n)$'s behave over certain averages just as the prime counting von Mangoldt function $\Lambda(n)$ does or is conjectured to do. We also…
In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…
Using results from the theory of modular forms, we reprove and extend a result of Romik about lacunary recurrence relations for Eisenstein series.
Given a sequence of complex square matrices, $a_n$, consider the sequence of their partial products, defined by $p_n=p_{n-1}a_{n}$. What can be said about the asymptotics as $n\to\infty$ of the sequence $f(p_n)$, where $f$ is a continuous…
We derive a functional central limit theorem (fclt) for normalised sums of a function of the partial sums of independent and identically distributed random variables. In particular, we show, using a technique presented in Huang and Zhang…
Let $F \subseteq [0,1]$ be a set that supports a probability measure $\mu$ with the property that $ |\widehat{\mu}(t)| \ll (\log |t|)^{-A}$ for some constant $ A > 0 $. Let $\mathcal{A}= (q_n)_{n\in \mathbb{N}} $ be a sequence of natural…
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.