Related papers: A probabilistic model of X-ray computed tomography

The aim of this paper is to present a new proof of an explicit version of the Berry-Ess\'{e}en type inequality of Bolthausen (Zeitschrift f\"ur Wahrscheinlichkeitstheorie und Verwandte Gebiete, 66, 379--386, 1984). The literature already…

Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…

In this article, we are interested in the high dimensional normal approximation of $T_n =\Big(\sum_{i=1}^{n}X_{i1}/\Big(\sqrt{\sum_{i=1}^{n}X_{i1}^2}\Big),\dots,$ $\sum_{i=1}^{n}X_{ip}/\Big(\sqrt{\sum_{i=1}^{n}X_{ip}^2}\Big)\Big)$ in…

Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained from X by dividing each row of X by its sum.…

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of…

This paper deals with the numerical approximation of normalizing constants produced by particle methods, in the general framework of Feynman-Kac sequences of measures. It is well-known that the corresponding estimates satisfy a central…

An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on…

Let $X_n=\sum_{i=1}^{\infty}a_i\epsilon_{n-i}$, where the $\epsilon_i$ are i.i.d. with mean 0 and at least finite second moment, and the $a_i$ are assumed to satisfy $|a_i|=O(i^{-\beta})$ with $\beta >1/2$. When $1/2<\beta<1$, $X_n$ is…

We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…

In this study we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson-Cowan equation can be obtained as the limit in probability on compacts for a sequence of microscopic models when the number…

In this paper, we analyze the random fluctuations in a one dimensional stochastic homogenization problem and prove a central limit result, i.e., the first order fluctuations can be described by a Gaussian process that solves an SPDE with…

We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these…

Let $X_1, X_2,\dots$ be a short-memory linear process of random variables. For $1\leq q<2$, let $\cF$ be a bounded set of real-valued functions on $[0,1]$ with finite $q$-variation. It is proved that…

In this paper, we introduce a fundamental model for independent and identically distributed sequence with model uncertainty on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels. Thanks…

In this paper, we propose a monotone approximation scheme for a class of fully nonlinear degenerate partial integro-differential equations (PIDEs) which characterize the nonlinear $\alpha$-stable L\'{e}vy processes under sublinear…

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then…

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range…

Applying Stein's method, an inductive technique and size bias coupling yields a Berry-Esseen theorem for normal approximation without the usual restriction that the coupling be bounded. The theorem is applied to counting the number of…

Let $r=r(n)$ be a sequence of integers such that $r\leq n$ and let $X_1,\ldots,X_{r+1}$ be independent random points distributed according to the Gaussian, the Beta or the spherical distribution on $\mathbb{R}^n$. Limit theorems for the…