Related papers: Limit theorems for moving averages of discretized …

We consider the moderate deviations behaviors for two (co-) volatility estima-tors: generalised bipower variation, Hayashi-Yoshida estimator. The results are obtained by using a new result about the moderate deviations principle for…

We study the estimation of moments and joint moments of microstructure noise. Estimators of arbitrary order of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide…

Let $\alpha$ be a Steinhaus or a Rademacher random multiplicative function. For a wide class of multiplicative functions $f$ we show that the sum $\sum_{n \le x}\alpha(n) f(n)$, normalised to have mean square $1$, has a non-Gaussian…

Let A(n) be a sequence of i.i.d. topical (i.e. isotone and additively homogeneous) operators. Let $x(n,x_0)$ be defined by $x(0,x_0)=x_0$ and $x(n,x_0)=A(n)x(n-1,x_0)$. This can modelize a wide range of systems including, task graphs, train…

In this paper we study supercritical super-OU processes with general branching mechanisms satisfying a second moment condition. We establish central limit theorems for the super-OU processes. In the small and crtical branching rate cases,…

This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…

This work focuses on the temporal average of the backward Euler--Maruyama (BEM) method, which is used to approximate the ergodic limit of stochastic ordinary differential equations with super-linearly growing drift coefficients. We give the…

In this paper we introduce the \textit{multivariate} Brownian semistationary (BSS) processes and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for…

In this paper, we obtain some uniform laws of large numbers and functional central limit theorems for sequential empirical measure processes indexed by classes of product functions satisfying appropriate Vapnik-Chervonenkis properties.

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks…

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.

For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The convergence takes place in the space of…

We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…

In this paper, we study almost sure central limit theorems for multiple stochastic integrals and provide a criterion based on the kernel of these multiple integrals. We apply our result to normalized partial sums of Hermite polynomials of…

We consider the limiting behavior of fluctuations of small noise diffusions with multiple scales around their homogenized deterministic limit. We allow full dependence of the coefficients on the slow and fast motion. These processes arise…

Let $Q$ be a transition probability on a measurable space $E$, let $(X\_n)\_n$ be a Markov chain associated to $Q$, and let $\xi$ be a real-valued measurable function on $E$, and $S\_n = \sum\_{k=1}^{n} \xi(X\_k)$. Under functional…

The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range…

We provide verification theorems (at different levels of generality) for infinite horizon stochastic control problems in continuous time for semimartingales. The control framework is given as an abstract "martingale formulation", which…