Related papers: The Mann-Whitney U-statistic for $\alpha$-dependen…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a…
We study a multivariate Hawkes process with long-range interactions, where the interaction strength decays as a power-law in the distance of the particles with exponent $1+\alpha.$ Our main focus is on the long-time asymptotic behavior of…
In this paper we introduce a model which provides a new approach to the phenomenon of stochastic resonance. It is based on the study of the properties of the stationary distribution of the underlying stochastic process. We derive the…
This paper proves that, under a monotonicity condition, the invariant probability measure of a McKean--Vlasov process can be approximated by weighted empirical measures of some processes including itself. These processes are described by…
We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
In this contribution, we introduce a general class of car-following models with an input-state-output port-Hamiltonian structure. We derive stability conditions and long-term behavior of the finite system with periodic boundaries and…
Moving from univariate to bivariate jointly dependent long-memory time series introduces a phase parameter $(\gamma)$, at the frequency of principal interest, zero; for short-memory series $\gamma=0$ automatically. The latter case has also…
The danger of confusing long-range dependence with non-stationarity has been pointed out by many authors. Finding an answer to this difficult question is of importance to model time-series showing trend-like behavior, such as river run-off…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
This article aims to consider a new univariate nonparametric cumulative sum (CUSUM) control chart for small shift of location based on both change-point model and Mann-Whitney statistic. Some comparisons on the performances of the proposed…
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
We identify general conditions under which regenerative processes with dependent cycles and cycle lengths are asymptotically independent. The result is applied to various models. In particular, independent L\'evy processes with dependent…
Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert…
In this paper, we propose a class of monitoring statistics for a mean shift in a sequence of high-dimensional observations. Inspired by the recent U-statistic based retrospective tests developed by Wang et al.(2019) and Zhang et al.(2020),…
We propose a general framework of sequential testing procedures based on $U$-statistics which contains as an example a sequential CUSUM test based on differences in mean but also includes a robust sequential Wilcoxon change point procedure.…
We consider the bifurcation problem $u'' + \lambda u = N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term which may also depend on the eigenvalue $\lambda$. We give a variational characterization of the…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…