Publications related to Sampling and (Sparse) Stochastic Processes: A Tale of Splines and Innovation

Methods of approximation influence aquatic ecosystem metabolism estimates

Aquatic ecologists have recently employed dynamic models to estimate aquatic ecosystem metabolism. All approaches involve numerically solving a differential equation describing dissolved oxygen (DO) dynamics. Although the DO differential equation can be so ...

Association for the Sciences of Limnology and Oceanography2016

Multi-index Monte Carlo: when sparsity meets sampling

Fabio Nobile

We propose and analyze a novel Multi Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a s ...

2016

‪Stochastic Control-A Moment Approach to Sparse Control Design‬

We consider design of sparse controllers for a stochastic linear system with infinite horizon quadratic objective. We formulate the non-sparse optimal solution through a semidefinite program for the second order moments of the states and inputs. Given that ...

University of Minnesota2016

Compressibility of Symmetric-α-Stable Processes

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

Within a deterministic framework, it is well known that n-term wavelet approximation rates of functions can be deduced from their Besov regularity. We use this principle to determine approximation rates for symmetric-α-stable (SαS) stochastic processes. Fi ...

IEEE2015

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. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolera ...

2015

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

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Michaël Unser, Virginie Sophie Uhlmann

Cardinal Hermite exponential spline functions are a generalization of the classical cardinal Hermite polynomial splines. In this work we consider the 4-dimensional space

ε _{ 4 }

= {1, x,

e ^{ \alpha x }

,

e ^{ -\alpha x }

} with α ∈ $ ℝ ^{ + } ...

SMAI-SIGMA2014

Estimation of phase derivatives using discrete energy separation algorithm in digital holographic interferometry

Pramod Rastogi, Rishikesh Dilip Kulkarni

This Letter proposes a new method for the estimation of the first-and second-order phase derivatives corresponding to strain and curvature from a single fringe pattern in digital holographic interferometry. The method is based on a discrete energy separati ...

Optical Soc Amer2014

PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise

Assyr Abdulle, Gilles Vilmart

A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by t ...

Elsevier2013

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

Christophe-Aschkan Mery

This project offers a rigorous introduction to the tools needed to construct a continuous stochastic process. Among other things, we give a very detailed proof of the Kolmogorov continuity criterion. We then construct a Brownian Motion following the formal ...

EPFL2013

Sampling and (Sparse) Stochastic Processes: A Tale of Splines and Innovation

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Methods of approximation influence aquatic ecosystem metabolism estimates

Multi-index Monte Carlo: when sparsity meets sampling

‪Stochastic Control-A Moment Approach to Sparse Control Design‬

Compressibility of Symmetric-α-Stable Processes

A continuation multilevel Monte Carlo algorithm

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Estimation of phase derivatives using discrete energy separation algorithm in digital holographic interferometry

PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

‪Stochastic Control-A Moment Approach to Sparse Control Design‬

Compressibility of Symmetric-α-Stable Processes

Methods of approximation influence aquatic ecosystem metabolism estimates

STOCHASTIC PROCESSES AND CONSTRUCTION OF BROWNIAN MOTION

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise

Multi-index Monte Carlo: when sparsity meets sampling

A continuation multilevel Monte Carlo algorithm

Estimation of phase derivatives using discrete energy separation algorithm in digital holographic interferometry