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Compressibility of Symmetric-α-Stable Processes

Publications associées (37)

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High weak order methods for stochastic equations based on modified equations

Assyr Abdulle, Gilles Vilmart, David Cohen

Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrat ...

Siam Publications2012

Numerical methods for stochastic partial differential equations with multiple scales

Assyr Abdulle, Grigorios A. Pavliotis

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, An ...

2012

Left-inverses of fractional Laplacian and sparse stochastic processes

Michaël Unser

The fractional Laplacian (-Delta)(gamma/2) commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0 < gamma < d, its inver ...

Springer2012

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

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

Propagation Models for Biochemical Reaction Networks

Maria-Emanuela-Canini Mateescu

In this thesis we investigate different ways of approximating the solution of the chemical master equation (CME). The CME is a system of differential equations that models the stochastic transient behaviour of biochemical reaction networks. It does so by d ...

EPFL2011

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

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

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

Stochastic modelling of prey depletion processes

Anthony Christopher Davison

The modelling of prey-predator interactions is of major importance for the understanding of population dynamics. Classically, these interactions are modelled using ordinary differential equations, but this has the drawbacks of assuming continuous populatio ...

2009