相关论文: Note on limit distribution of normalized return ti…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic…

In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying…

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…

We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case the accumulated…

This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We obtain criteria for the exponential convergence to a unique quasi-stationary distribution in total…

Although viral spreading processes taking place in networks are often analyzed using Markovian models in which both the transmission and the recovery times follow exponential distributions, empirical studies show that, in many real…

We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…

In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…

By using the large deviation principle, we investigate the expected exit time from the interval [-1,1] of a process of autoregressive type. The case when the autoregression function f is linear and the innovations have a normal distribution…

We prove that for any $\alpha$-mixing stationnary process the hitting time of any $n$-string $A_n$ converges, when suitably normalized, to an exponential law. We identify the normalization constant $\lambda(A_n)$. A similar statement holds…

We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a…

We describe the statistics of repetition times of a string of symbols in a stochastic process. Denote by T(A) the time elapsed until the process spells the finite string A and by S(A) the number of consecutive repetitions of A. We prove…

We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only…

We study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial…

In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall…

In this paper, we consider an expanding construction of a distributed control system, which is obtained by adding a new subsystem one after the other, until all $n$ subsystems, where $n \ge 2$, are included in the distributed control…

In this paper we prove two results. First we show that dynamical systems with a $\phi$-mixing measure have in the limit Poisson distributed return times almost everywhere. We use the Chen-Stein method to also obtain rates of convergence.…

In order to characterize the fluctuation between the ergodic limit and the time-averaging estimator of a full discretization in a quantitative way, we establish a central limit theorem for the full discretization of the parabolic stochastic…

In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient…