Related papers: Empirical Processes of Multidimensional Systems wi…

Let $(\tau_n)$ be a sequence of toral automorphisms $\tau_n : x \rightarrow A_n x \hbox{mod}\ZZ^d$ with $A_n \in {\cal A}$, where ${\cal A}$ is a finite set of matrices in $SL(d, \mathbb{Z})$. Under some conditions the method of…

In this paper, a fourth moment bound for partial sums of functional of strongly ergodic Markov chain is established. This type of inequality plays an important role in the study of empirical process invariance principle. This one is…

Consider a stochastic process $\{X(t)\}$ on a finite state space $ {\sf X}=\{1,\dots, d\}$. It is conditionally Markov, given a real-valued `input process' $\{\zeta(t)\}$. This is assumed to be small, which is modeled through the scaling,…

This paper considers functional central limit theorems for stationary absolutely regular mixing processes. Bounds for the entropy with bracketing are derived using recent results in Nickl and P\"otscher (2007). More specifically, their…

In this paper, we establish a joint (bivariate) functional central limit theorem of the sample quantile and the $r$-th absolute centred sample moment for functionals of mixing processes. More precisely, we consider $L_2$-near epoch…

We prove a central limit theorem for stationary multiple (random) fields of martingale differences $f\circ T_{\underline{i}}$, $\underline{i}\in \Bbb Z^d$, where $T_{\underline{i}}$ is a $\Bbb Z^d$ action. In most cases the multiple…

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…

The main objective of this article is to establish a central limit theorem for additive three-variable functionals of bifurcating Markov chains. We thus extend the central limit theorem under point-wise ergodic conditions studied in…

We consider "randomized" statistics constructed by using a finite number of observations a random field at randomly chosen points. We generalize the invariance principle (the functional CLT), the Glivenko--Cantelli theorem, the theorem…

This paper aims to establish a central limit theorem for Markov processes conditioned not to be absorbed under a very general assumption on quasi-stationarity for the underlying process. To do so, a central limit theorem has been…

We establish functional limit theorems for ergodic sums of observables with power singularities for expanding circle maps. In the regime where the observables have infinite variance, we show that when rescaled by $N^{1/s}(\ln N)^\alpha$,…

A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals…

We present a general functional central limit theorem started at a point also known under the name of quenched. As a consequence, we point out several new classes of stationary processes, defined via projection conditions, which satisfy…

We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the Central Limit Theorems formally established for their marginal empirical…

Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…

We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…

There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes $...,X_{-1},X_0,X_1,...$ whose partial sums $S_n=X_1+...+X_n$ are of the form $S_n=M_n+R_n$, where $M_n$ is a square…

We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying L\'{e}vy measures. The limit process is a new class of symmetric stable…

Using Stein's method, we prove an abstract result that yields multivariate central limit theorems with a rate of convergence for time-dependent dynamical systems. As examples we study a model of expanding circle maps and a quasistatic…

We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving $\|\sum_{k=1} ^nf\circ \theta^k\|_2$, improving previous results. Then, using known results on martingale…