Publications related to An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Michaël Unser, Julien René Pierre Fageot

Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...

SPRINGER/PLENUM PUBLISHERS2019

A central limit theorem for functions of stationary max-stable random fields on R-d

Erwan Fabrice Koch, Clément Dombry

Max-stable random fields are very appropriate for the statistical modelling of spatial extremes. Hence, integrals of functions of max-stable random fields over a given region can play a key role in the assessment of the risk of natural disasters, meaning t ...

ELSEVIER2019

Dynamic Average Diffusion With Randomized Coordinate Updates

Ali H. Sayed, Bicheng Ying, Kun Yuan

This work derives and analyzes an online learning strategy for tracking the average of time-varying distributed signals by relying on randomized coordinate-descent updates. During each iteration, each agent selects or observes a random entry of the observa ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

Robert Dalang, Thomas Marie Jean-Baptiste Humeau

We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric Levy white noise, with symmetric alpha-stable Levy white noise as an important special case. We identify con ...

UNIV WASHINGTON, DEPT MATHEMATICS2019

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Assyr Abdulle, Giacomo Garegnani

A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...

MATHICSE2018

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation (PDE) with a random coefficient solved with the stochastic collocation finite element method (SC-FEM). The random diffusion coefficient is assumed to depend in an affine way on independent ...

2018

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Fei Pu

In this thesis, we study systems of linear and/or non-linear stochastic heat equations and fractional heat equations in spatial dimension

1

driven by space-time white noise. The main topic is the study of hitting probabilities for the solutions to these ...

EPFL2018

Chebyshev Inequalities for Products of Random Variables

Daniel Kuhn, Napat Rujeerapaiboon, Wolfram Wiesemann

We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...

2018

Asynchronous adaptive networks

Ali H. Sayed

In a recent article [1] we surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in response to streamin ...

Elsevier2018

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

2018

An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data

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Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

A central limit theorem for functions of stationary max-stable random fields on R-d

Dynamic Average Diffusion With Randomized Coordinate Updates

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Chebyshev Inequalities for Products of Random Variables

Asynchronous adaptive networks

Stable high-order randomized cubature formulae in arbitrary dimension

A central limit theorem for functions of stationary max-stable random fields on R-d

Stable high-order randomized cubature formulae in arbitrary dimension

Dynamic Average Diffusion With Randomized Coordinate Updates

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Asynchronous adaptive networks

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Chebyshev Inequalities for Products of Random Variables