Publications related to Long-range dependence

Roughness Evolution Induced by Third-Body Wear

Jean-François Molinari, Tobias Brink, Antonio Joaquin Garcia Suarez

Surface roughness is a key factor when it comes to friction and wear, as well as to other physical properties. These phenomena are controlled by mechanisms acting at small scales, in which the topography of apparently flat surfaces is revealed. Roughness i ...

2024

Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields

Cheuk Yin Lee

We establish a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local nondeterm ...

INT STATISTICAL INST2023

On the probability distribution of the local times of diagonally operator-self-similar Gaussian fields with stationary increments

Thomas Mountford, Kamran Kalbasi

In this paper, we study the local times of vector-valued Gaussian fields that are 'diagonally operator-selfsimilar' and whose increments are stationary. Denoting the local time of such a Gaussian field around the spatial origin and over the temporal unit h ...

INT STATISTICAL INST2020

The probability of intransitivity in dice and close elections

Jan Hazla

We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to 1/2, that a throw from one die is higher than the other. We ...

2020

Semiparametric Bayesian Risk Estimation for Complex Extremes

Thomas Lugrin

Extreme events are responsible for huge material damage and are costly in terms of their human and economic impacts. They strike all facets of modern society, such as physical infrastructure and insurance companies through environmental hazards, banking an ...

EPFL2018

Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures

Emeric Rolland Georges Thibaud, Raphaël Huser

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect depen ...

Elsevier Sci Ltd2017

Bayesian uncertainty management in temporal dependence of extremes

Anthony Christopher Davison, Thomas Lugrin, Jonathan A. Tawn

Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long-and short-range dependence of extremes may both appear. In applications, an assum ...

Springer Verlag2016

Feynman-Kac representation for the parabolic Anderson model driven by fractional noise

Thomas Mountford, Kamran Kalbasi

We consider the parabolic Anderson model driven by fractional noise: partial derivative/partial derivative t u(t,x) = k Delta u(t,x) + u(t,x)partial derivative/partial derivative t W(t,x) x is an element of Z(d), t >= 0, where k > 0 is a diffusion constant ...

Academic Press Inc Elsevier Science2015

Discrete stochastic heat equation driven by fractional noise : Feynman-Kac representation and asymptotic behavior

Kamran Kalbasi

We consider the parabolic Anderson model on

\mathbb{Z}^d

driven by fractional noise. We prove that it has a mild solution given by Feynman-Kac representation which coincides with the partition function of a directed polymer in a fractional Brownian envir ...

EPFL2014

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

Michaël Unser, Arash Amini, Pouya Dehghani Tafti, Hagay Kirshner

This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of stochastic differential equations driven by white Levy innovations. These are completely specified ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Contributions to Spatial Statistics : Species Distributions and Rare Events

Emeric Rolland Georges Thibaud

This thesis proposes some contributions to the spatial modelling of species distributions and extreme values. Predictive models are increasingly used to model the distribution of species and to estimate the potential effects of global change on biodiversit ...

EPFL2014

Fractional Brownian motion and anomalous diffusion in vibrated granular materials

Daniele Mari, Gérard Gremaud, Alessandro Luigi Sellerio

We propose a new approach to the study of diffusion dynamics in vibrated granular systems. The dynamic of a granular material is mainly defined by dry friction interactions. This type of interaction is difficult to model for a large quantity of particles. ...

2012

The autocorrelation function for island areas on self-affine surfaces

Jean-François Molinari, Guillaume Anciaux, Srinivasa Babu Ramisetti

The spatial distribution of regions that lie above contours of constant height through a self-affine surface is studied as a function of the Hurst exponent H. If the surface represents a landscape, these regions correspond to islands. When the surface repr ...

2011

Fractional Brownian Models For Vector Field Data

Michaël Unser, Pouya Dehghani Tafti

In this note we introduce a vector generalization of fractional Brownian motion. Our definition takes into account directional properties of vector fields-such as divergence, rotational behaviour, and interactions with coordinate transformations-that have ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Fractional Brownian Vector Fields

Michaël Unser, Pouya Dehghani Tafti

This work puts forward an extended definition of vector fractional Brownian motion (fBm) using a distribution theoretic formulation in the spirit of Gel′fand and Vilenkin's stochastic analysis. We introduce random vector fields that share the statistical i ...

SIAM2010

Time-Intensity Superposition for Photoinitiated Polymerization of Fluorinated and Hyperbranched Acrylate Nanocomposites

Yves Leterrier, Sara Dalle Vacche, Valérie Geiser

The validity of the time-intensity superposition principle for the photoinitiated polymerization of nanocomposites based on a monofunctional fluorinated acrylate and on a multifunctional hyperbranched polyether acrylate was investigated in this work. Maste ...

2010

Holder properties of local times for fractional Brownian motions

Thomas Mountford, Driss Baraka

We study the local times of fractional Brownian motions for all temporal dimensions, N, spatial dimensions d and Hurst parameters H for which local times exist. We establish a Holder continuity result that is a refinement of Xiao (Probab Th Rel Fields 109: ...

Springer-Verlag2009

Modeling all exceedances above a threshold using an extremal dependence structure: Inferences on several flood characteristics

Flood quantile estimation is of great importance for several types of engineering studies and policy decisions. However, practitioners must often deal with the limited availability of data and with short-length observation series. Thus, the information mus ...

American Geophysical Union2009

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti

In this contribution, we study the notion of affine invariance (specifically, invariance to the shifting, scaling, and rotation of the coordinate system) as a starting point for the development of mathematical tools and approaches useful in the characteriz ...

IEEE2009

Propriétés fines des trajectoires du mouvement brownien fractionnaire

Driss Baraka

Let X = {X(t); t ∈ RN} be a (N,d) fractional Brownian motion in Rd of index H ∈ (0,1). We study the local time of X for all temporal dimensions N and spatial dimensions d for which local time exist. We obtain two main results : R1. If we denote by Lx(I) th ...

EPFL2008