Publication

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

Publications associées (17)

Stochastic particle transport by deep-water irregular breaking waves

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, ...

Cambridge University Press2023

Propagation of singularities for the stochastic wave equation

Cheuk Yin Lee

We study the existence and propagation of singularities of the solution to a one-dimensional linear stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. Our approach is based on a simultaneous law of the ...

ELSEVIER2022

The Hausdorff measure of the range and level sets of Gaussian random fields with sectorial local nondeterminism

Cheuk Yin Lee

We determine the exact Hausdorff measure functions for the range and level sets of a class of Gaussian random fields satisfying sectorial local nondeterminism and other assumptions. We also establish a Chung-type law of the iterated logarithm. The results ...

INT STATISTICAL INST2022

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

Normal approximation of the solution to the stochastic heat equation with Levy noise

Carsten Hao Ye Chong

Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...

SPRINGER2020

The Almost-Sure Asymptotic Behavior Of The Solution To The Stochastic Heat Equation With Levy Noise

Carsten Hao Ye Chong

We examine the almost-sure asymptotics of the solution to the stochastic heat equation driven by a Levy space-time white noise. When a spatial point is fixed and time tends to infinity, we show that the solution develops unusually high peaks over short tim ...

INST MATHEMATICAL STATISTICS2020

Dating Death: An Empirical Comparison of Medical Underwriters in the U.S. Life Settlements Market

Jiahua Xu

The value of a life settlement investment, manifested through a traded life insurance policy, is highly dependent on the insured's life expectancy (LE). LE estimation in life settlements relies heavily on medical underwriting. Employing different evaluatio ...

2020

On the Size of K-Cross-Free Families

János Pach, Andrei Kupavskii, Istvan Tomon

Two subsets A,B of an n-element ground set X are said to be crossing, if none of the four sets AB, A\B, B\A and X(AB) are empty. It was conjectured by Karzanov and Lomonosov forty years ago that if a family F of subsets of X does not contain k pairwise cr ...

SPRINGER HEIDELBERG2019

Global Solutions To Stochastic Reaction-Diffusion Equations With Super-Linear Drift And Multiplicative Noise

Robert Dalang, Davar Khoshnevisan

Let xi(t, x) denote space-time white noise and consider a reaction-diffusion equation of the form ...

INST MATHEMATICAL STATISTICS2019

Stochastic partial differential equations driven by Lévy white noises : generalized random processes, random field solutions and regularity

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

Moments And Growth Indices For The Nonlinear Stochastic Heat Equation With Rough Initial Conditions

Robert Dalang, Le Chen

We study the nonlinear stochastic heat equation in the spatial domain R, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be a measure on R, such as the Dirac delta function, but th ...

Inst Mathematical Statistics2015

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

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

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

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

Extended Formulations, Nonnegative Factorizations, and Randomized Communication Protocols

Hans Raj Tiwary, Yuri Faenza

We show that the binary logarithm of the nonnegative rank of a nonnegative matrix is, up to small constants, equal to the minimum complexity of a randomized communication protocol computing the matrix in expectation. We use this connection to prove new con ...

Springer Berlin Heidelberg2012

Stochastic Models for Sparse and Piecewise-Smooth Signals

Michaël Unser, Pouya Dehghani Tafti

We introduce an extended family of continuous-domain stochastic models for sparse, piecewise-smooth signals. These are specified as solutions of stochastic differential equations, or, equivalently, in terms of a suitable innovation model; the latter is ana ...

IEEE2011

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

A law of the iterated logarithm for fractional Brownian motions

Driss Baraka, Thomas Mountford

We show that for a class of Gaussian processes indexed by one dimensional time, the local times obey the behavior conjectured by Xiao. ...

2008