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Stochastic partial differential equation

Publications associées (158)

Explicit methods for stiff stochastic differential equations

Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...

Springer-Verlag Berlin2012

Stochastic integrals for spde's: A comparison

Robert Dalang

We present the Walsh theory of stochastic integrals with respect to martingale measures, and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of stochastic integrals with respect to Hilbert-space-valued Wiener processes, and ...

Elsevier2011

Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty

Jan Sickmann Hesthaven, Zhen Gao

The important task of evaluating the impact of random parameters on the output of stochastic ordinary differential equations (SODE) can be computationally very demanding, in particular for problems with a high-dimensional parameter space. In this work we c ...

GLOBAL SCIENCE PRESS2011

On the efficiency of numerical homogenization methods

Assyr Abdulle

The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of num ...

EMS2011

Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty

Jan Sickmann Hesthaven, Zhen Gao

We discuss adaptive sparse grid algorithms for stochastic differential equations with a particular focus on applications to electromagnetic scattering by structures with holes of uncertain size, location, and quantity. Stochastic collocation (SC) methods a ...

Elsevier2011

Link between Alginate Reaction Front Propagation and General Reaction Diffusion Theory

Jürgen Brugger, Philippe Renaud, Thomas Michael Braschler, Kristopher Pataky, Ana Valero, Ludovica Colella

We provide a common theoretical framework reuniting specific models for the Ca2+-alginate system and general reaction diffusion theory along with experimental validation on a microfluidic chip. As a starting point, we use a set of nonlinear, partial differ ...

2011

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

Ecohydrological Footprints

Samir Suweis

Ecohydrological footprints are defined as the response of ecosystem functions or services to changes in their hydrologic drivers. In this thesis, several diverse footprints are addressed: noise-driven effects on storage-discharge relations and catchment st ...

EPFL2011

High performance computing for partial differential equations

Vincent Keller, Jonas Marcel Lätt, Etienne Ahusborde

When representing realistic physical phenomena by partial differential equations (PDE), it is crucial to approximate the underlying physics correctly, to get precise results, and to efficiently use the computer architecture. Incorrect results can appear in ...

2011

Jump-diffusions in Hilbert spaces: existence, stability and numerics

Damir Filipovic

By means of an original approach, called 'method of the moving frame', we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential equations (SPDEs) with path-dependent coefficients driven by an i ...

2010

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