Related papers: Almost sure invariance principle for random piecew…
We give rates of convergence in the almost sure invariance principle for sums of dependent random variables with semi exponential tails, whose coupling coefficients decrease at a subexponential rate. We show that the rates in the strong…
The Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
For a class of symmetric random matrices whose entries are martingale differences adapted to an increasing filtration, we prove that under a Lindeberg-like condition, the empirical spectral distribution behaves asymptotically similarly to a…
We consider families of transformations in multidimensional Riemannian manifolds with non-uniformly expanding behavior. We give sufficient conditions for the continuous variation (in the $L^1$-norm) of the densities of absolutely continuous…
In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…
In this paper, we prove the strong convergence theorems for nearly nonexpansive mappings, using the modified Picard-Mann hybrid iteration process in the context of uniformly convex Banach space.
We describe a robust methodology, based on the martingale argument of Nachmias and Peres and random walk estimates, to obtain simple upper and lower bounds on the size of a maximal component in several random graphs \textit{at criticality}.…
A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…
Consider a real-valued branching random walk in the boundary case. Using the techniques developed by A\"id\'ekon and Shi [5], we give two integral tests which describe respectively the lower limits for the minimal position and the upper…
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
In scientific disciplines such as neuroimaging, climatology, and cosmology it is useful to study the uncertainty of excursion sets of imaging data. While the case of imaging data obtained from a single study condition has already been…
We study the long-term behavior of the iteration of a random map consisting of Lipschitz transformations on a compact metric space, independently and randomly selected according to a fixed probability measure. Such a random map is said to…
For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n}…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…
Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…
This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem for a sequene of nearly nonexpansive mappings with respect to a nonexpansive mapping. It is shown that under…
We consider a free fermion chain with uniform nearest-neighbor hopping and let it evolve from an arbitrary initial state with a fixed macroscopic number of particles. We then prove that, at a sufficiently large and typical time, the…
We obtain results concerning the so-called factorization for the convergence of random variables almost everywhere (almost surely or with probability one), belonging to the classical Lebesgue-Riesz spaces and we extend these results to the…