Related papers: A study of counts of Bernoulli strings via conditi…
We propose a statistical model for networks of event count sequences built on a cascade structure. We assume that each event triggers successor events, whose counts follow additive probability distributions; the ensemble of counts is given…
We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index $\alpha \in (0,1]$ and the service completions are triggered by an independent fractional Poisson…
A Bernoulli random walk is a random trajectory starting from 0 and having i.i.d. increments, each of them being $+1$ or -1, equally likely. The other families cited in the title are Bernoulli random walks under various conditionings. A peak…
We give recurrences, generating functions and explicit exact expressions for the enumeration of fundamental quantities involving runs in binary strings. We first focus on enumerations concerning runs of ones, and we then analyse the same…
Iterated quadratic polynomials give rise to a rich collection of different dynamical systems that are parametrized by a simple complex parameter $c$. The different dynamical features are encoded by the \emph{kneading sequence} which is an…
Given a homogeneous Poisson process on ${\mathbb{R}}^d$ with intensity $\lambda$, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that…
Dynamical scaling is an asymptotic property typical for the dynamics of first-order phase transitions in physical systems and related to self-similarity. Based on the integral-representation for the marginal probabilities of a fractional…
In this note, we study a class of random subsets of positive integers induced by Bernoulli random variables. We obtain sufficient conditions such that the random set is almost surely lacunary, does not have bounded gaps and contains…
We introduce data structures answering queries concerning the occurrences of patterns from a given dictionary $\mathcal{D}$ in fragments of a given string $T$ of length $n$. The dictionary is internal in the sense that each pattern in…
This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying…
We investigate a spatial random graph model whose vertices are given as a marked Poisson process on $\mathbb{R}^d$. Edges are inserted between any pair of points independently with probability depending on the spatial displacement of the…
Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…
In this paper we consider the fractional parts of a general sequence, for example the sequence $\alpha \sqrt{n}$ or $\alpha n^2$. We give a general method, which allows one to show that long-range correlations (correlations where the…
We consider random walks associated with conductances on Delaunay triangulations, Gabriel graphs and skeletons of Voronoi tilings which are generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on point processes and…
For a sequence of i.i.d. $d$-dimensional random vectors with independent continuously distributed coordinates, say that the $n$th observation in the sequence sets a record if it is not dominated in every coordinate by an earlier…
We consider here together the inference questions and the change-point problem in Poisson autoregressions (see Tj{\o}stheim, 2012). The conditional mean (or intensity) of the process is involved as a non-linear function of it past values…
This paper deals with the complexity of strings, which play an important role in biology (nucleotid sequences), information theory and computer science. The d-complexity of a string is defined as the number of its distinct d-substrings…
An existing dialogue between number theory and dynamical systems is advanced. A combinatorial device gives necessary and sufficient conditions for a sequence of non-negative integers to count the periodic points in a dynamical system. This…
Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…
Let $X$, $B$ and $Y$ be three Dirichlet, Bernoulli and beta independent random variables such that $X\sim \mathcal{D}(a_0,...,a_d),$ such that $\Pr(B=(0,...,0,1,0,...,0))=a_i/a$ with $a=\sum_{i=0}^da_i$ and such that $Y\sim \beta(1,a).$ We…