Related papers: Long-Range Correlations of Sequences Modulo 1
The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation…
We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a…
Suppose that $k$ series, all having the same autocorrelation function, are observed in parallel at $n$ points in time or space. From a single series of moderate length, the autocorrelation parameter $\beta$ can be estimated with limited…
We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
This paper develops a more general theory of sequences of dependent categorical random variables, extending the works of Korzeniowski (2013) and Traylor (2017) that studied first-kind dependency in sequences of Bernoulli and categorical…
We say that a sequence $\{x_n\}_{n \geq 1}$ in $[0,1)$ has Poissonian pair correlations if \begin{equation*} \lim_{N \rightarrow \infty} \frac{1}{N} \# \left\{ 1 \leq l \neq m \leq N \, : \, \left\lVert x_l-x_m \right\rVert < \frac{s}{N}…
Basic results in combinatorial mathematics provide the foundation for a theory and calculus for reasoning about sequential behavior. A key concept of the theory is a generalization of Boolean implicant which deals with statements of the…
Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view…
We have provided a fractional generalization of the Poisson renewal processes by replacing the first time derivative in the relaxation equation of the survival probability by a fractional derivative of order $\alpha ~(0 < \alpha \leq 1)$. A…
We consider convergence properties of the long-term behaviors with respect to the coefficient of the stochastic term for a nonautonomous stochastic $p$-Laplacian lattice equation with multiplicative noise. First, the upper semi-continuity…
We study the correlations of the celebrated Sine$_\beta$ point process. This point process arises as the bulk scaling limit of $\beta$-ensembles and has a geometric description through the Brownian carousel, as shown by Valk\'o and Vir\'ag…
We present the general relationship between phase correlations and the hierarchy of polyspectra in the Fourier space, and the new theoretical understanding of the phase information is provided. Phase correlations are related to the…
The article determines the asymptotic shape of the extremal clusters in stationary regularly varying random fields. To deduce this result, we present a general framework for the Poisson approximation of point processes on Polish spaces…
With our ability to record more neurons simultaneously, making sense of these data is a challenge. Functional connectivity is one popular way to study the relationship between multiple neural signals. Correlation-based methods are a set of…
In this work, we study the partial sums of independent and identically distributed random variables with the number of terms following a fractional Poisson (FP) distribution. The FP sum contains the Poisson and geometric summations as…
We say that a string of length $d$ occurs, in a Bernoulli sequence, if a success is followed by exactly $(d-1)$ failures before the next success. The counts of such $d$-strings are of interest, and in specific independent Bernoulli…
We study the asymptotic behaviour of partial sums of long range dependent random variables and that of their counting process, together with an appropriately normalized integral process of the sum of these two processes, the so-called…
We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…
Let $\{X_{k,i};i\geq 1,k\geq 1\}$ be an array of i.i.d. random variables and let $\{p_n;n\geq 1\}$ be a sequence of positive integers such that $n/p_n$ is bounded away from 0 and $\infty$. For $W_n=\max_{1\leq i<j\leq…