Publications by Robert Dalang | EPFL Graph Search

Sample Path Regularity of Non-autonomous Uniformly Parabolic Spdes

We consider a stochastic PDE driven by a parabolic second order partial differential operator with non-constant coefficients and with a nonlinear random external forcing given by a Gaussian noise that is white in time and spatially homogeneous. We prove th ...

SPRINGER2025

Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Robert Dalang, Fei Pu

We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

Springer/Plenum Publishers2024

Power variations in fractional Sobolev spaces for a class of parabolic stochastic PDEs

Robert Dalang, Carsten Hao Ye Chong

We consider a class of parabolic stochastic PDEs on bounded domains D c Rd that includes the stochastic heat equation but with a fractional power gamma of the Laplacian. Viewing the solution as a process with values in a scale of fractional Sobolev spaces ...

INT STATISTICAL INST2023

Polarity Of Almost All Points For Systems Of Nonlinear Stochastic Heat Equations In The Critical Dimension

Robert Dalang

We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, ...

INST MATHEMATICAL STATISTICS-IMS2021

Optimal lower bounds on hitting probabilities for non-linear systems of stochastic fractional heat equations

Robert Dalang, Fei Pu

We consider a system of d non-linear stochastic fractional heat equations in spatial dimension 1 driven by multiplicative d-dimensional space-time white noise. We establish a sharp Gaussian-type upper bound on the two-point probability density function of ...

ELSEVIER2021

Multiple points of Gaussian random fields

Robert Dalang, Cheuk Yin Lee

This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of Dalang et al. (2017), we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical dimensions. The result ...

INST MATHEMATICAL STATISTICS-IMS2021

Hausdorff dimension of the boundary of bubbles of additive Brownian motion and of the Brownian sheet

Robert Dalang, Thomas Mountford

We first consider the additive Brownian motion process (X(s(1), s(2)), (s(1), s(2)) is an element of R-2) defined by X(s(1), s(2)) = Z(1)(s(1)) - Z2(s2), where Z(1) and Z(2) are two independent (two-sided) Brownian motions. We show that with probability 1, ...

POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN2021

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k >= 1

Robert Dalang, Fei Pu

We establish a sharp estimate on the negative moments of the smallest eigenvalue of the Malliavin matrix gamma z of Z := (u(s, y), u(t , x) - u(s, y)), where u is the solution to a system of d non-linear stochastic heat equations in spatial dimension k >= ...

UNIV WASHINGTON, DEPT MATHEMATICS2020

On the density of the supremum of the solution to the linear stochastic heat equation

Robert Dalang, Fei Pu

We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of densities for locally nondegenerate random variables, we establish the smoot ...

SPRINGER2020

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