Publications related to Macroscopic stability for nonfinite range kernels

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

Approximating Functions On Stratified Sets

We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced class of stochasti ...

Amer Mathematical Soc2015

Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes

Adrian Blumenthal

Stochastic models that account for sudden, unforeseeable events play a crucial role in many different fields such as finance, economics, biology, chemistry, physics and so on. That kind of stochastic problems can be modeled by stochastic differential equat ...

EPFL2015

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

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

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

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

MATHICSE Technical Report : Moment equations for the mixed formulation of the Hodge Laplacian with stochastic data

Fabio Nobile, Annalisa Buffa, Francesca Bonizzoni

We study the mixed formulation of the stochastic Hodge-Laplace problem defined on a n-dimensional domain D (

n \geq 1

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

MATHICSE2012

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization

Laura Vinckenbosch

The topic of this thesis is the study of several stochastic control problems motivated by sailing races. The goal is to minimize the travel time between two locations, by selecting the fastest route in face of randomly changing weather conditions, such as ...

EPFL2012

Macroscopic stability for nonfinite range kernels

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

Approximating Functions On Stratified Sets

Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes

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

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

MATHICSE Technical Report : Moment equations for the mixed formulation of the Hodge Laplacian with stochastic data

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization

Approximating Functions On Stratified Sets

Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes

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

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

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

MATHICSE Technical Report : Moment equations for the mixed formulation of the Hodge Laplacian with stochastic data

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization

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

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

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION