Publications related to MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

Erik Gustaf Bogislaw Von Schwerin, Hakon Andreas Hoel

We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both b ...

Siam Publications2014

Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

2014

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The CMLMC algorithm so ...

MATHICSE2014

A study of the spatio-temporal behaviour of bed load transport rate fluctuations

Joris Heyman

This thesis addresses the problem of a statistical description of the transport of sediment as bed load. It highlights the role of fluctuations arising during the transport process, and their impact on macroscopic averages. The results presented here are b ...

EPFL2014

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Fabio Nobile, Lorenzo Tamellini

In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number

N

of random inputs and an analytic dependence of the s ...

2014

MATHICSE Technical Report : Analytic regularity and collocation approximation for PDEs with random domain deformations

Fabio Nobile

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remap ...

MATHICSE2013

Density approximations for multivariate affine jump-diffusion processes

Damir Filipovic

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial mom ...

Elsevier2013

A stochastic collocation method for the second order wave equation with a discontinuous random speed

Fabio Nobile

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and ...

Springer Verlag2013

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...

Siam Publications2013

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection led and consider a stochas ...

Society for Industrial and Applied Mathematics2013

MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

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On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

Perturbation analysis for the Darcy problem with log-normal permeability

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

A study of the spatio-temporal behaviour of bed load transport rate fluctuations

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

MATHICSE Technical Report : Analytic regularity and collocation approximation for PDEs with random domain deformations

Density approximations for multivariate affine jump-diffusion processes

A stochastic collocation method for the second order wave equation with a discontinuous random speed

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

MATHICSE Technical Report : Analytic regularity and collocation approximation for PDEs with random domain deformations

A stochastic collocation method for the second order wave equation with a discontinuous random speed

A study of the spatio-temporal behaviour of bed load transport rate fluctuations

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Density approximations for multivariate affine jump-diffusion processes

Perturbation analysis for the Darcy problem with log-normal permeability

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations