Related papers: A weak convergence result for sequential empirical…
The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but…
For a strictly stationary sequence of $\mathbb{R}_{+}^{d}$--valued random vectors we derive functional convergence of partial maxima stochastic processes under joint regular variation and weak dependence conditions. The limit process is an…
We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…
We show weak convergence of quantile and expectile processes to Gaussian limit processes in the space of bounded functions endowed with an appropriate semimetric which is based on the concepts of epi- and hypo convergence as introduced in…
We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is…
This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary foundation…
We consider the convergence of empirical processes indexed by functions that depend on an estimated parameter $\eta$ and give several alternative conditions under which the ``estimated parameter'' $\eta_n$ can be replaced by its natural…
We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions…
The functional autoregressive model is a Markov model taylored for data of functional nature. It revealed fruitful when attempting to model samples of dependent random curves and has been widely studied along the past few years. This…
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…
The aim of this paper is to extend the aggregation convergence results given in (Dacunha-Castelle and Fermin 2005, Dacunha-Castelle and Fermin 2008) to doubly stochastic linear and nonlinear processes with weakly dependent innovations.…
A random walk in random scenery $(Y_n)_{n\in\mathbb{N}}$ is given by $Y_n=\xi_{S_n}$ for a random walk $(S_n)_{n\in\mathbb{N}}$ and iid random variables $(\xi_n)_{n\in\mathbb{Z}}$. In this paper, we will show the weak convergence of the…
In this paper, we prove a large deviation principle for the empirical measures of a system of weakly interacting diffusion with reflection. We adopt the weak convergence approach. To make this approach work, we show that the sequence of…
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…
In the seminal contribution [4] the joint weak convergence of maxima and minima of weakly dependent stationary sequences is derived under some mild asymptotic conditions. In this paper we address additionally the case of incomplete samples…
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is…
This paper develops a general concentration inequality for the suprema of empirical processes with dependent data. The concentration inequality is obtained by combining generic chaining with a coupling-based strategy. Our framework…
We first establish strong convergence rates for multiscale systems driven by $\alpha$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four…