Related papers: Stable Central Limit Theorems for Super Ornstein-U…

We consider sequences of random variables whose probability generating functions are polynomials all of whose roots lie on the unit circle. The distribution of such random variables has only been sporadically studied in the literature. We…

Suppose that $X=(X_{t})_{t\ge 0}$ is either a general supercritical non-local branching Markov process, or a general supercritical non-local superprocess, on a Luzin space. Here, by ``supercritical" we mean that the mean semigroup of $X$…

We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for…

We establish stable functional central limit theorems for scaled elephant random walks in the diffusive, critical, and superdiffusive cases using the martingale approach.

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…

This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…

In this short communication we present a (functional) central limit theorem for the idle process of a one-sided reflected Ornstein-Uhlenbeck proces.

In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…

This paper establishes a functional stable central limit theorem for a class of superdiffusive solutions to stochastic differential equations driven by an $\alpha$-stable process.

The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as…

We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…

In this paper, we provide a central limit theorem for the finite-dimensional marginal distributions of empirical processes $(Z_n(f))_{f\in\mathcal{F}}$ whose index set $\mathcal{F}$ is a family of cluster functionals valued on blocks of…

We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by such a noise. Our main contribution is on the…

This is a continuation, and conclusion, of our study of bounded solutions $u$ of the semilinear parabolic equation $u_t=u_{xx}+f(u)$ on the real line whose initial data $u_0=u(\cdot,0)$ have finite limits $\theta^\pm$ as $x\to\pm\infty$. We…

Let $(\mathbb X, T)$ be a subshift of finite type equipped with the Gibbs measure $\nu$ and let $f$ be a real-valued H\"older continuous function on $\mathbb X$ such that $\nu(f) = 0$. Consider the Birkhoff sums $S_n f = \sum_{k=0}^{n-1} f…

We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…

This paper studies one-dimensional Ornstein-Uhlenbeck processes, with the distinguishing feature that they are reflected on a single boundary (put at level 0) or two boundaries (put at levels 0 and d>0). In the literature they are referred…

We prove that uniform second order growth, tilt stability, and strong metric regularity of the limiting subdifferential --- three notions that have appeared in entirely different settings --- are all essentially equivalent for any…

Let $(X_i,i\geq 1)$ be a sequence of i.i.d. random variables with values in $[0,1]$, and $f$ be a function such that $`E(f(X_1)^2)<+\infty$. We show a functional central limit theorem for the process $t\mapsto \sum_{i=1}^n f(X_i)1_{X_i\leq…