Related papers: Convergence of Point Processes with Weakly Depende…

This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…

For a strictly stationary sequence of $\mathbb{R}_{+}^{d}$--valued random vectors we derive functional convergence of partial maxima stochastic processes under joint regular variation and weak dependence conditions. The limit process is an…

We consider a dynamic version of the Neyman contagious point process that can be used for modelling the spacial dynamics of biological populations, including species invasion scenarios. Starting with an arbitrary finite initial…

We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential…

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…

In this paper, a special sequence of controlled branching processes is considered. We provide a simple set of sufficient conditions for the weak convergence of such processes to a weak solution to a kind of continuous branching processes…

This paper explores certain kinds of empirical process with respect to the components of multivariate Gaussian. We put forward some finite sample bounds which hold for multivariate Gaussian under general dependence. We give necessary and…

Let $\{Y_i,-\infty<i<\infty\}$ be a doubly infinite sequence of identically distributed, negatively dependent random variables under sub-linear expectations, $\{a_i,-\infty<i<\infty\}$ be an absolutely summable sequence of real numbers. In…

We derive a necessary and sufficient condition for stochastic processes to have almost periodic finite dimensional distributions; in particular, we obtain characterizations for infinitely divisible processes to be almost periodic in terms…

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…

Let $\left\{ Z_{n},n=0,1,2,...\right\} $ be a critical branching process in random environment and let $\left\{ S_{n},n=0,1,2,...\right\} $ be its associated random walk. It is known that if the increments of this random walk belong…

This article employs the relation between probabilities of two consecutive values of a Poisson random variable to derive conditions for the weak convergence of point processes to a Poisson process. As applications, we consider the starting…

We consider the simple random walk on random graphs generated by discrete point processes. This random graph has a random subset of a cubic lattice as the vertices and lines between any consecutive vertices on lines parallel to each…

We study the sequential empirical process indexed by general function classes and its smoothed set-indexed analogue. Sufficient conditions for asymptotic equicontinuity are provided for nonstationary arrays of time series. This yields…

Motivated by some common-change point tests, we investigate the asymptotic distribution of the U-statistic process $U_n(t)=\sum_{i=1}^{[nt]}\sum_{j=[nt]+1}^n h(X_i,X_j)$, $0\leq t\leq 1$, when the underlying data are long-range dependent.…

We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…

(English) This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary…

We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of…

This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…

We consider a limit theorem for a triangular array of point processes generated by non-identically distributed random variables, and apply the result for the analysis of the limiting behavior of the Argmaximum of independent random…