Publications related to Stochastic integrals for spde's: A comparison

High order numerical approximation of the invariant measure of ergodic SDEs

We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then pre ...

Society for Industrial and Applied Mathematics2014

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

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

Thumbnail galleries for procedural models

Mark Pauly, Pablo Federico Mueller, Boris Neubert, Stefan Lienhard

Procedural modeling allows for the generation of innumerable variations of models from a parameterized, conditional or stochastic rule set. Due to the abstractness, complexity and stochastic nature of rule sets, it is often very difficult to have an unders ...

Wiley-Blackwell2014

Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

Le Chen

In this thesis, we study several stochastic partial differential equations (SPDE’s) in the spatial domain R, driven by multiplicative space-time white noise. We are interested in how rough and unbounded initial data affect the random field solution and the ...

EPFL2013

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Gilles Brunner

In this project, we study and compare two methods to solve stochastic ordinary differential equations. The first is the Monte Carlo method and the second uses Polynomial Chaos. In the first part, we will solve a stochastic ordinary differential equation by ...

2013

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Michaël Unser, Emrah Bostan, Ulugbek Kamilov, Masih Nilchian

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes, which specifies cont ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Alfio Quarteroni, Peng Chen

Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...

Elsevier Science Sa2013

Coupling reduced basis and numerical homogenization methods for solving quasilinear elliptic problems

Assyr Abdulle

The workshop has brought together experts in the broad field of partial differential equations with highly heterogeneous coefficients. Analysts and computational and applied mathematicians have shared results and ideas on a topic of considerable interest b ...

EMS2013

Stochastic integrals for spde's: A comparison

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High order numerical approximation of the invariant measure of ergodic SDEs

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

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

Thumbnail galleries for procedural models

Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Coupling reduced basis and numerical homogenization methods for solving quasilinear elliptic problems

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

Accurate and efficient evaluation of failure probability for partial different equations with random input data

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

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

High order numerical approximation of the invariant measure of ergodic SDEs

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

Coupling reduced basis and numerical homogenization methods for solving quasilinear elliptic problems

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

Thumbnail galleries for procedural models