Publications related to Approximating Functions On Stratified Sets

Analysis and computation of the elastic wave equation with random coefficients

We analyze the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics of some given ...

2015

Upper bounds for the reach-avoid probability via robust optimization

Maryam Kamgarpour, John Lygeros, Tyler Summers

We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by restricting attentio ...

2015

Ellipse-Preserving Hermite Interpolation and Subdivision

Michaël Unser

We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve with the ability t ...

Elsevier2015

Compressibility of Symmetric-α-Stable Processes

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

Within a deterministic framework, it is well known that n-term wavelet approximation rates of functions can be deduced from their Besov regularity. We use this principle to determine approximation rates for symmetric-α-stable (SαS) stochastic processes. Fi ...

IEEE2015

On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

Fabio Nobile

In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assum ...

2014

High order numerical approximation of the invariant measure of ergodic SDEs

Assyr Abdulle, Gilles Vilmart

We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then pre ...

Society for Industrial and Applied Mathematics2014

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part I: Continuous-Domain Theory

Michaël Unser, Pouya Dehghani Tafti

We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by some generalized ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term

Fabio Nobile, Annalisa Buffa, Francesca Bonizzoni

We study the mixed formulation of the stochastic Hodge-Laplace problem dened on a

n

-dimensional domain

D (n ≥ 1)

, with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three dimensional case. We ...

2014

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

Christophe-Aschkan Mery

This project offers a rigorous introduction to the tools needed to construct a continuous stochastic process. Among other things, we give a very detailed proof of the Kolmogorov continuity criterion. We then construct a Brownian Motion following the formal ...

EPFL2013

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Jean-Yves Le Boudec

Assume that a stochastic process can be approximated, when some scale parameter gets large, by a fluid limit (also called mean field limit", or hydrodynamic limit"). A common practice, often called the ``fixed point approximation" consists in approxima ...

2013

Approximating Functions On Stratified Sets

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Analysis and computation of the elastic wave equation with random coefficients

Upper bounds for the reach-avoid probability via robust optimization

Ellipse-Preserving Hermite Interpolation and Subdivision

Compressibility of Symmetric-α-Stable Processes

On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

High order numerical approximation of the invariant measure of ergodic SDEs

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part I: Continuous-Domain Theory

Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Ellipse-Preserving Hermite Interpolation and Subdivision

High order numerical approximation of the invariant measure of ergodic SDEs

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part I: Continuous-Domain Theory

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Analysis and computation of the elastic wave equation with random coefficients

On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term

Upper bounds for the reach-avoid probability via robust optimization

Compressibility of Symmetric-α-Stable Processes