On the Besov regularity of periodic Levy noises

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Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

PoGaIN: Poisson-Gaussian Image Noise Modeling From Paired Samples

Sabine Süsstrunk, Majed El Helou, Kaan Okumus

Image noise can often be accurately fitted to a Poisson-Gaussian distribution. However, estimating the distribution parameters from a noisy image only is a challenging task. Here, we study the case when paired noisy and noise-free samples are accessible. N ...

IEEE Institute of Electrical and Electronics Engineers2022

Supersymmetries in nonequilibrium Langevin dynamics

Elisabeth Agoritsas

Stochastic phenomena are often described by Langevin equations, which serve as a mesoscopic model for microscopic dynamics. It has been known since the work of Parisi and Sourlas that reversible (or equilibrium) dynamics present supersymmetries (SUSYs). Th ...

2021

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

Nicolas Henri Bernard Flammarion, Scott William Pesme, Loucas Pillaud-Vivien

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear networks through i ...

2021

Low Noise Clock Generation: Modeling, Analysis and Implementation

Duygu Kostak

The aim of this thesis is to implement, analyze and improve the selected low noise clock generation and distribution techniques for ADC implementations. The thesis is divided into two parts. The first part focuses on the sampling phase generation and distr ...

EPFL2021

Deterministic error bounds for kernel-based learning techniques under bounded noise

Colin Neil Jones, Paul Scharnhorst, Emilio Maddalena

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and epsilon-support vector regression. By assuming the ground-truth function belongs to th ...

2021

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 ...

2020

Normalized Gaussian path integrals

Giulio Corazza

Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show ...

AMER PHYSICAL SOC2020

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 ...

2020

The Almost-Sure Asymptotic Behavior Of The Solution To The Stochastic Heat Equation With Levy Noise

Carsten Hao Ye Chong

We examine the almost-sure asymptotics of the solution to the stochastic heat equation driven by a Levy space-time white noise. When a spatial point is fixed and time tends to infinity, we show that the solution develops unusually high peaks over short tim ...

INST MATHEMATICAL STATISTICS2020

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Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022