Related papers: Central limit theorems for branching processes und…

We solve the problem of constructing an asymptotic global confidence region for the means and the covariance matrices of the reproduction distributions involved in a supercritical multitype branching process. Our approach is based on a…

We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of…

In this work we investigate limit theorems for the time-averaged process $\left(\frac{1}{t}\int_0^t X_s^x ds\right)_{t\geq 0}$ where $X^x$ is a subcritical continuous-state branching processes with immigration (CBI processes) starting in $x…

For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…

We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case…

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…

Given a Coxeter system of large type we prove a non--commutative central limit theorem: After normalisation with the square root of n the characteristic function of the set of the first n generators tends in distribution to Wigners…

In this paper we consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in R^d and undergoing a binary, supercritical branching with a constant rate \lambda>0. This system is known to…

We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the…

In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain Burgers' equation and the stochastic reaction-diffusion equation. The weak…

In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…

This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…

We consider sub-critical configuration models and show that the central limit theorem for any additive statistic holds when the statistics satisfies a fourth moment assumption, a variance lower bound and the degree sequence of graph…

We give a generalization of the ergodic theorem for semi-Markov linear-type processes. This generalization is proved for the case when a common support of distributions defining this process is not arithmetic. Also we give an uniform…

We establish limit theorems involving weak convergence of multiple generations of critical and supercritical branching processes. These results arise naturally when dealing with the joint asymptotic behavior of functionals defined in terms…

Consider a supercritical Crump-Mode-Jagers process $(\mathcal{Z}_{t}^{\varphi})_{t \geq 0}$ counted with a random characteristic $\varphi$ that depends on an individual's life and their descendant process up to a fixed generation. Under…

The goal of this paper is to describe conditions which guarantee a central limit theorem for random variables, which distributions are controled by hidden Markov chains. We proved that when a Markov chain is ergodic and random variables…

We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $\nu$ and $\mu$ supported on $\mathbb{R}^d$ such that $\mu$ is the reversible measure of a diffusion process. In order to…

The stationary asymptotic properties of the diffusion limit of a multi-type branching process with neutral mutations are studied. For the critical and subcritical processes the interesting limits are those of quasi-stationary distributions…

We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than {\epsilon} ({\epsilon} > 0). It is known ([BM05]) that the empirical measure of these fragments converges in law, under some…