Related papers: A complete characterization of a correlated Bernou…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
A complete characterization of the asymptotic singularity probability of random circulant Bernoulli matrices is given for all values of the probability parameter.
We introduce a one-dimensional random walk, which at each step performs a reinforced dynamics with probability $\theta$ and with probability $1 - \theta$, the random walk performs a step independent of the past. We analyse its asymptotic…
We consider a standard one-dimensional Brownian motion on the time interval $[0,1]$ conditioned to have vanishing iterated time integrals up to order $N$. We show that the resulting processes can be expressed explicitly in terms of shifted…
In this paper, we develop a new method to estimate the parameters of a deteriorating system under perfect condition-based maintenance. This method is based on the asymptotical behavior of the system, which is studied by using the renewal…
In this paper, by establishing a Borel-Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random…
We consider Bernoulli bond percolation on a large scale-free tree in the supercritical regime, meaning informally that there exists a giant cluster with high probability. We obtain a weak limit theorem for the sizes of the next largest…
We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior…
We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is…
The main result of the article reads: the distribution of a continuous starting from zero local martingale whose quadratic characteristic is almost surely absolutely continuous with respect to some non-random increasing continuous function…
Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…
In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…
The asymptotic behaviour of a closed BCMP network, with $n$ queues and $m_n$ clients, is analyzed when $n$ and $m_n$ become simultaneously large. Our method relies on Berry-Esseen type approximations coming in the Central Limit Theorem. We…
We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the…
We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states…
We consider the perturbed Mann's iterative process \begin{equation} x_{n+1}=(1-\theta_n)x_n+\theta_n f(x_n)+r_n, \end{equation} where $f:[0,1]\rightarrow[0,1]$ is a continuous function, $\{\theta_n\}\in [0,1]$ is a given sequence, and…
Our goal is to investigate the asymptotic behavior of the center of mass of the elephant random walk, which is a discrete-time random walk on integers with a complete memory of its whole history. In the diffusive and critical regimes, we…
The theory of random matrices contains many central limit theorems. We have central limit theorems for eigenvalues statistics, for the log-determinant and log-permanent, for limiting distribution of individual eigenvalues in the bulk, and…
We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping in the sense of P\'olya and Szeg\"o, so the error incurred in truncating the series is of the same sign as the next…
In his, by now, classical work from 1981, Nerman made extensive use of a crucial martingale $(W_t)_{t \geq 0}$ to prove convergence in probability, in mean and almost surely, of supercritical general branching processes (a.k.a.…