Related papers: Discrete rough paths and limit theorems

The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…

Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…

We consider the infinite directed graph with vertices the set of integers ...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or value "minus infinity". Consider random weights v(j,k), indexed by pairs (j,k) of…

General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…

In this paper we present some new asymptotic results for high frequency statistics of Brownian semi-stationary processes. More precisely, we will show that singularities in the weight function, which is one of the ingredients of a BSS…

We explore an asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.

The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and…

In this paper, we consider a "compensated" random sum that arises from numerical approximation of stochastic integrations and differential equations. We show that the compensated sum exhibits some surprising cancellations among its…

The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter…

We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality…

Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are…

We investigate the asymptotic properties of permutations drawn from the Luce model, a natural probabilistic framework in which permutations are generated sequentially by sampling without replacement, with selection probabilities…

We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…

Based on a martingale theory approach, we present a complete characterization of the asymptotic behaviour of a lazy reinforced random walk (LRRW) which shows three different regimes (diffusive, critical and superdiffusive). This allows us…

This paper provides estimates for the convergence rate of the total variation distance in the framework of the Breuer-Major theorem, assuming some smoothness properties of the underlying function. The results are proved by applying new…

We look at geometric limits of large random non-uniform permutations. We mainly consider two theories for limits of permutations: permuton limits, introduced by Hoppen, Kohayakawa, Moreira, Rath, and Sampaio to define a notion of scaling…

Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a functional, an estimate for different probability distances…

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…