Publications related to The n-term Approximation of Periodic Generalized Levy Processes

Max-stable processes and stationary systems of Levy particles

We study stationary max-stable processes {n(t): t is an element of R} admitting a representation of the form n(t) = max(i is an element of N) (U-i +Y-i(t)), where Sigma(infinity)(i=1) delta U-i is a Poisson point process on R with intensity e(-u)du, and Y1 ...

Elsevier2015

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

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

Michaël Unser, Arash Amini, Pouya Dehghani Tafti, Hagay Kirshner

This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of stochastic differential equations driven by white Levy innovations. These are completely specified ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Invariant manifolds with boundary for jump-diffusions

Damir Filipovic

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random measures. ...

Univ Washington, Dept Mathematics2014

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Michaël Unser, Julien René Pierre Fageot, Emrah Bostan

We study the statistics of wavelet coefficients of non-Gaussian images, focusing mainly on the behaviour at coarse scales. We assume that an image can be whitened by a fractional Laplacian operator, which is consistent with an

∥ω∥ ^{ -\gamma }

spectral ...

IEEE2014

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Jean-Yves Le Boudec

Assume that a stochastic process can be approximated, when some scale parameter gets large, by a fluid limit (also called mean field limit", or hydrodynamic limit"). A common practice, often called the ``fixed point approximation" consists in approxima ...

2013

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

Michaël Unser, Pedram Pad

Sinusoidal transforms such as the DCT are known to be optimal-that is, asymptotically equivalent to the Karhunen-Loeve transform (KLT)-for the representation of Gaussian stationary processes, including the classical AR(1) processes. While the KLT remains a ...

Ieee2013

On the Optimality of Operator-Like Wavelets for Sparse AR(1) Processes

Michaël Unser, Pedram Pad

Sinusoidal transforms such as the DCT are known to be optimal—that is, asymptotically equivalent to the Karhunen-Loève transform (KLT)—for the representation of Gaussian stationary processes, including the classical AR(1) processes. While the KLT remains ...

IEEE2013

FORWARD BROWNIAN MOTION

We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at -∞ 1. We show that these processes do not have to have the distribution of st ...

2012

The Analog Formulation of Sparsity Implies Infinite Divisibility and Rules Out Bernoulli-Gaussian Priors

Michaël Unser, Arash Amini, Ulugbek Kamilov

Motivated by the analog nature of real-world signals, we investigate continuous-time random processes. For this purpose, we consider the stochastic processes that can be whitened by linear transformations and we show that the distribution of their samples ...

Ieee2012

The n-term Approximation of Periodic Generalized Levy Processes

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Max-stable processes and stationary systems of Levy particles

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

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

Invariant manifolds with boundary for jump-diffusions

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

On the Optimality of Operator-Like Wavelets for Sparse AR(1) Processes

FORWARD BROWNIAN MOTION

The Analog Formulation of Sparsity Implies Infinite Divisibility and Rules Out Bernoulli-Gaussian Priors

Max-stable processes and stationary systems of Levy particles

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

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

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Invariant manifolds with boundary for jump-diffusions

On the Optimality of Operator-Like Wavelets for Sparse AR(1) Processes

FORWARD BROWNIAN MOTION

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

The Analog Formulation of Sparsity Implies Infinite Divisibility and Rules Out Bernoulli-Gaussian Priors