Related papers: Limit theorems for record indicators in threshold …

We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…

We consider renewal processes where events, which can for instance be the zero crossings of a stochastic process, occur at random epochs of time. The intervals of time between events, $\tau_{1},\tau_{2},...$, are independent and identically…

Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…

The most general exclusion single species one dimensional reaction-diffusion models with nearest-neighbor interactions which are both autonomous and can be solved exactly through full interval method are introduced. Using a generating…

Willems' fundamental lemma enables data-driven analysis and control by characterizing an unknown system's behavior directly in terms of measured data. In this work, we extend a recent frequency-domain variant of this result--previously…

Let $(X_{n,i})_{1\le i\le n,n\in\mathbb{N}}$ be a triangular array of row-wise stationary $\mathbb{R}^d$-valued random variables. We use a "blocks method" to define clusters of extreme values: the rows of $(X_{n,i})$ are divided into $m_n$…

In this article, we consider a sequence $(N_n)_{n \geq 1}$ of point processes, whose points lie in a subset $E$ of $\bR \verb2\2 \{0\}$, and satisfy an asymptotic independence condition. Our main result gives some necessary and sufficient…

In this paper is proved the limit theorem for randomly indexed sequence of random processes in the case where sequences of random index and random processes are independent, also the estimation of convergence rate is obtained.

We derive a necessary and sufficient condition for the sum of M independent continuous random variables modulo 1 to converge to the uniform distribution in L^1([0,1]), and discuss generalizations to discrete random variables. A consequence…

Numerical and analytical results are presented for the maximal relative height distribution of stationary periodic Gaussian signals (one dimensional interfaces) displaying a 1/f^alpha power spectrum. For 0<alpha<1 (regime of decaying…

In this article we consider a natural class of random walks on free products of graphs, which arise as convex combinations of random walks on the single factors. From the works of Gilch [6,7] it is well-known that for these random walks the…

We study the fluctuation behavior of individual eigenvalues of kernel matrices arising from dense graphon-based random graphs. Under minimal integrability and boundedness assumptions on the graphon, we establish distributional limits for…

We study weak convergence of empirical processes of dependent data $(X_i)_{i\geq0}$, indexed by classes of functions. Our results are especially suitable for data arising from dynamical systems and Markov chains, where the central limit…

A variant of self-similar approximation theory is suggested, permitting an easy and accurate summation of divergent series consisting of only a few terms. The method is based on a power-law algebraic transformation, whose powers play the…

In this paper, we investigate the problem of classifying feature vectors with mutually independent but non-identically distributed elements. First, we show the importance of this problem. Next, we propose a classifier and derive an…

We introduce a continuous-time random walk model on an infinite multilayer structure inspired by transportation networks. Each layer is a copy of $\mathbb{R}^d$, indexed by a non-negative integer. A walker moves within a layer by means of…

We consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoregressive coefficient tends to one, the noise scaling…

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…

We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature…

The goal of this expository article is a fairly self-contained account of some averaging processes of functions along sequences of the form $(\alpha^n x)^{}_{n\in\mathbb{N}}$, where $\alpha$ is a fixed real number with $| \alpha | > 1$ and…