Concept

Donsker's theorem

Related publications (24)

A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

In this paper we use the Riemann zeta distribution to give a new proof of the Erdos-Kac Central Limit Theorem. That is, if zeta(s) = Sigma(n >= 1) (1)(s)(n) , s > 1, then we consider the random variable X-s with P(X-s = n) = (1) (zeta) ( ...

Providence2023

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Victor Panaretos, Neda Mohammadi Jouzdani

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

Amsterdam2023

A central limit theorem for functions of stationary max-stable random fields on R-d

Erwan Fabrice Koch, Clément Dombry

Max-stable random fields are very appropriate for the statistical modelling of spatial extremes. Hence, integrals of functions of max-stable random fields over a given region can play a key role in the assessment of the risk of natural disasters, meaning t ...

ELSEVIER2019

Stochastic partial differential equations driven by Lévy white noises

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

Fréchet means in Wasserstein space

Yoav Zemel

This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces,

\mathcal W_2 ( \mathbb R^d )

. This question arises naturally from the problem of separating amplitude and phase variation i ...

EPFL2017

Functional Central Limit Theorem for the Interface of the Symmetric Multitype Contact Process

Thomas Mountford, Daniel Rodrigues Valesin

We study the interface of the symmetric multitype contact process on Z. In this process, each site of Z is either empty or occupied by an individual of one of two species. Each individual dies with rate 1 and attempts to give birth with rate 2R lambda; the ...

Impa2016

Amplitude And Phase Variation Of Point Processes

Victor Panaretos, Yoav Zemel

We develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping, known as the problem of separation of amplitude and phase variation. The amplitude variation of a real random function {Y(x) : x ...

Institute of Mathematical Statistics2016

Sources and forms of modelling uncertainties for structural identification

Ian Smith, Romain Pasquier

The aim of model-based structural identification is to make sense of monitoring data in order to improve knowledge of the real behaviour of structures. Common use of structural-identification techniques involves an assumption of independent zero-mean Gauss ...

2015

Statistical-thermodynamics modelling of the built environment in relation to urban ecology

Jean-Louis Scartezzini, Nahid Mohajeri Pour Rayeni

Various aspects of the built environment have important effects on ecology. Providing suitable metrics for the built forms so as to quantify and model their internal relations and external ecological footprints, however, remains a challenge. Here we provid ...

Elsevier2015

Quantitative Version Of The Kipnis-Varadhan Theorem And Monte Carlo Approximation Of Homogenized Coefficients

Jean-Christophe Mourrat

This article is devoted to the analysis of a Monte Carlo method to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. We consider the case of independent and identically distributed coefficients, and adopt the p ...

Inst Mathematical Statistics2013

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Fréchet means in Wasserstein space

Yoav Zemel

This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces,

\mathcal W_2 ( \mathbb R^d )

. This question arises naturally from the problem of separating amplitude and phase variation i ...

EPFL2017