Publications related to The non-linear stochastic wave equation in high dimensions

Path properties of the solution to the stochastic heat equation with Levy noise

Robert Dalang, Carsten Hao Ye Chong, Thomas Marie Jean-Baptiste Humeau

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

SPRINGER2019

Decompositions Of Log-Correlated Fields With Applications

Janne Matias Junnila

In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. Th ...

2019

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

Robert Dalang, Thomas Marie Jean-Baptiste Humeau

We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric Levy white noise, with symmetric alpha-stable Levy white noise as an important special case. We identify con ...

UNIV WASHINGTON, DEPT MATHEMATICS2019

Feedback and Mediation in Causal Inference Illustrated by Stochastic Process Models

Mats Julius Stensrud

The concept of causality is naturally related to processes developing over time. Central ideas of causal inference like time-dependent confounding (feedback) and mediation should be viewed as dynamic concepts. We shall study these concepts in the context o ...

2018

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

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Jean-Philippe Lucien Montillet

Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Partial Differential Equations (PDEs) with a particular application to the wave equation [ 15]. To do so, the author ha ...

Int Center Scientific Research & Studies2017

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

MATHICSE2017

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

On the Besov regularity of periodic Levy noises

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

In this paper, we study the Besov regularity of Levy white noises on the d-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain regularity results for gene ...

Academic Press Inc Elsevier Science2017

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

Alfio Quarteroni, Andrea Manzoni, Federico Negri

The numerical solution of partial differential equations (PDEs) depending on para- metrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this compu ...

MATHICSE2016

The non-linear stochastic wave equation in high dimensions

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Path properties of the solution to the stochastic heat equation with Levy noise

Decompositions Of Log-Correlated Fields With Applications

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

Feedback and Mediation in Causal Inference Illustrated by Stochastic Process Models

Stochastic partial differential equations driven by Lévy white noises

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

On the Besov regularity of periodic Levy noises

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Decompositions Of Log-Correlated Fields With Applications

On the Besov regularity of periodic Levy noises

Path properties of the solution to the stochastic heat equation with Levy noise

Feedback and Mediation in Causal Inference Illustrated by Stochastic Process Models

Stochastic partial differential equations driven by Lévy white noises

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition