Publications related to Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

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

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

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Fei Pu

In this thesis, we study systems of linear and/or non-linear stochastic heat equations and fractional heat equations in spatial dimension

1

driven by space-time white noise. The main topic is the study of hitting probabilities for the solutions to these ...

EPFL2018

ON A GENERALIZATION OF THE POINCARE LEMMA TO EQUATIONS OF THE TYPE dw plus a Lambda w = f

David Valentin Strütt

We study the system of linear partial differential equations given by dw + a Lambda w = f, on open subsets of R-n, together with the algebraic equation da Lambda u = beta, where a is a given 1-form, f is a given (k + 1)-form, beta is a given k + 2-form, w ...

2018

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

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

Elisabetta Chiodaroli

We consider the initial value problem for the inviscid Primitive and Boussinesq equations in three spatial dimensions. We recast both systems as an abstract Eulertype system and apply the methods of convex integration of De Lellis and Székelyhidi to show t ...

2017

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

A posteriori error estimation for partial differential equations with random input data

Diane Sylvie Guignard

This thesis is devoted to the derivation of error estimates for partial differential equations with random input data, with a focus on a posteriori error estimates which are the basis for adaptive strategies. Such procedures aim at obtaining an approximati ...

EPFL2016

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

Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

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

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

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

ON A GENERALIZATION OF THE POINCARE LEMMA TO EQUATIONS OF THE TYPE dw plus a Lambda w = f

Feedback and Mediation in Causal Inference Illustrated by Stochastic Process Models

Stochastic partial differential equations driven by Lévy white noises

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

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

A posteriori error estimation for partial differential equations with random input data

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

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

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

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

ON A GENERALIZATION OF THE POINCARE LEMMA TO EQUATIONS OF THE TYPE dw plus a Lambda w = f

Feedback and Mediation in Causal Inference Illustrated by Stochastic Process Models

Stochastic partial differential equations driven by Lévy white noises

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

A posteriori error estimation for partial differential equations with random input data

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

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