Publications related to SPHARMA approximations for stationary functional time series on the sphere

The n-term Approximation of Periodic Generalized Levy Processes

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

SPRINGER/PLENUM PUBLISHERS2020

Gaussian and sparse processes are limits of generalized Poisson processes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Normal approximation of the solution to the stochastic heat equation with Levy noise

Carsten Hao Ye Chong

Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...

SPRINGER2020

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

Stationary time-vertex signal processing

Nathanaël Perraudin, Andreas Loukas

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some known graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity for short, that g ...

2019

Concentration compactness for critical radial wave maps

Joachim Krieger, Elisabetta Chiodaroli

We consider radially symmetric, energy critical wave maps from (1 + 2)-dimensional Minkowski space into the unit sphere

\mathbf{S}^m

, m≥1, and prove global regularity and scattering for classical smooth data of finite energy. In addition, we establish a ...

2018

Gaussian versus Sparse Stochastic Processes

Julien René Pierre Fageot

Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...

EPFL2017

Fréchet means in Wasserstein space

Yoav Zemel

This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces,

\mathcal W_2 ( \mathbb R^d )

. This question arises naturally from the problem of separating amplitude and phase variation i ...

EPFL2017

Bayesian Uncertainty Management in Temporal Dependence of Extremes

Anthony Christopher Davison, Thomas Lugrin, Jonathan A. Tawn

Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In applications, an assu ...

Springer Verlag2016

Bayesian uncertainty management in temporal dependence of extremes

Anthony Christopher Davison, Thomas Lugrin, Jonathan A. Tawn

Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long-and short-range dependence of extremes may both appear. In applications, an assum ...

Springer Verlag2016

SPHARMA approximations for stationary functional time series on the sphere

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The n-term Approximation of Periodic Generalized Levy Processes

Gaussian and sparse processes are limits of generalized Poisson processes

Normal approximation of the solution to the stochastic heat equation with Levy noise

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

Stationary time-vertex signal processing

Concentration compactness for critical radial wave maps

Gaussian versus Sparse Stochastic Processes

Fréchet means in Wasserstein space

Bayesian Uncertainty Management in Temporal Dependence of Extremes

Bayesian uncertainty management in temporal dependence of extremes

The n-term Approximation of Periodic Generalized Levy Processes

Gaussian and sparse processes are limits of generalized Poisson processes

Stationary time-vertex signal processing

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

Normal approximation of the solution to the stochastic heat equation with Levy noise

Concentration compactness for critical radial wave maps

Gaussian versus Sparse Stochastic Processes

Bayesian Uncertainty Management in Temporal Dependence of Extremes

Fréchet means in Wasserstein space

Bayesian uncertainty management in temporal dependence of extremes