Publications related to Stochastic Analysis of Some Expedited Forwarding Networks

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

Analysis and Design of Large-scale Online Classes

Martin Vetterli, Paolo Prandoni, Tao-Chun Lee

Massive Open Online Courses (MOOCs) have become an emergent paradigm of large-scale knowledge distribution, have generated wide interest in the higher education community and are anticipated by many to bring impact to the future of higher education. In thi ...

2014

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

MATHICSE Technical Report : Analysis and computation of the elastic wave equation with random coefficients

Fabio Nobile

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 ...

MATHICSE2012

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

Markov chains with discontinuous drifts have differential inclusion limits

Nicolas Gabriel Gast

In this paper, we study deterministic limits of Markov processes having discontinuous drifts. While most results assume that the limiting dynamics is continuous, we show that these conditions are not necessary to prove convergence to a deterministic system ...

Elsevier2012

Reliability Analysis of Data Storage Systems

Vinodh Venkatesan

Modern data storage systems are extremely large and consist of several tens or hundreds of nodes. In such systems, node failures are daily events, and safeguarding data from them poses a serious design challenge. The focus of this thesis is on the data rel ...

EPFL2012

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

Stochastic Analysis of Some Expedited Forwarding Networks

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

Analysis and Design of Large-scale Online Classes

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

MATHICSE Technical Report : Analysis and computation of the elastic wave equation with random coefficients

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

Markov chains with discontinuous drifts have differential inclusion limits

Reliability Analysis of Data Storage Systems

High weak order methods for stochastic equations based on modified equations

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

Analysis and Design of Large-scale Online Classes

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

MATHICSE Technical Report : Analysis and computation of the elastic wave equation with random coefficients

Markov chains with discontinuous drifts have differential inclusion limits

High weak order methods for stochastic equations based on modified equations

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

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

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

Reliability Analysis of Data Storage Systems