Related papers: On Convergence to Stochastic Integrals

Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the…

In this paper we propose an alternative to the coupling of Berkes, Liu and Wu [1] to obtain strong approximations for partial sums of dependent sequences. The main tool is a new Rosen-thal type inequality expressed in terms of the coupling…

Based on deleting-item central limit theory, the classical Donsker's theorem of partial-sum process of independent and identically distributed (i.i.d.) random variables is extended to incomplete partial-sum process. The incomplete…

This paper provides extensions of the work on subsampling by Bertail et al. (2004) for strongly mixing case to weakly dependent case by application of the results of Doukhan and Louhichi (1999). We investigate properties of smooth and rough…

We establish the rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution in terms of truncated pseudomoments by implementing the idea of Yu. Studnyev for getting…

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…

The paper introduces a general framework for statistical analysis of functional time series from a Bayesian perspective. The proposed approach, based on an extension of the popular dynamic linear model to Banach-space valued observations…

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

We study convergence and convergence rates for resampling schemes. Our first main result is a general consistency theorem based on the notion of negative association, which is applied to establish the almost-sure weak convergence of…

In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove…

By the approximation method introduced in \cite{FYW}, the existence and uniqueness are proved for a class of distribution-dependent stochastic functional differential equations (DDSFDEs). Moreover, combining the Harnack and shift-Harnack…

Divergence-form operators with random coefficients homogenize over large scales. Over the last decade, an intensive research effort focused on turning this asymptotic statement into quantitative estimates. The goal of this note is to review…

We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…

This article develops general conditions for weak convergence of adaptive Markov chain Monte Carlo processes and is shown to imply a weak law of large numbers for bounded Lipschitz continuous functions. This allows an estimation theory for…

A formal sum $\sum_n f(S_n)$ may be seen as the integral $\int f dN$ with respect to random point process $N(A)=|\{n:S_n\in A\}|$. We study its convergence beyond the well known context of Lebesgue integrable functions, admitting…

A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…

This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer…

Sparse functional data frequently arise in real-world applications, posing significant challenges for accurate classification. To address this, we propose a novel classification method that integrates functional principal component analysis…

Following Cs\"{o}rg\H{o}, Szyszkowicz and Wang (Ann. Statist. {\bf 34}, (2006), 1013--1044) we consider a long range dependent linear sequence. We prove weak convergence of the uniform Vervaat and the uniform Vervaat error processes,…

A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the…