Publications related to Perturbation analysis for the Darcy problem with log-normal permeability

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

We analyze the stability and accuracy of discrete least squares on multivariate poly- nomial spaces to approximate a given function depending on a multivariate random variable uniformly distributed on a hypercube. The polynomial approximation is calculated ...

MATHICSE2015

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

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

In this paper, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a para ...

MATHICSE2014

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

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

2014

Shortest-Weight Paths In Random Regular Graphs

Léo Hamed Amini

Consider a random regular graph with degree d and of size n. Assign to each edge an independent and identically distributed exponential random variable with mean one. In this paper we establish a precise asymptotic expression for the maximum number of edge ...

Siam Publications2014

MATHICSE Technical Report : 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 ...

MATHICSE2013

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

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

Perturbation analysis for the Darcy problem with log-normal permeability

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MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

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

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Shortest-Weight Paths In Random Regular Graphs

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

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

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

MATHICSE Technical Report : Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Shortest-Weight Paths In Random Regular Graphs

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

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

Density approximations for multivariate affine jump-diffusion processes

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

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

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