Publications related to Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

2024

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Victor Panaretos, Neda Mohammadi Jouzdani

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

Elsevier2024

On the asymptotic behavior of solutions to the Vlasov-Poisson system

Klaus Martin Widmayer

We prove small data modified scattering for the Vlasov-Poisson system in dimension

d=3

using a method inspired from dispersive analysis. In particular, we identify a simple asymptotic dynamic related to the scattering mass. ...

2022

The Error-Feedback Framework: Better Rates for SGD with Delayed Gradients and Compressed Updates

Sai Praneeth Reddy Karimireddy, Sebastian Urban Stich

We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two terms: (i) a stocha ...

Microtome Publishing2020

An overview of a new sensor calibration platform

Jan Skaloud, Stéphane Guerrier, Philipp Clausen

Inertial sensors are increasingly being employed in different types of applications. The reduced cost and the extremely small size makes them the number-one-choice in miniature embedded devices like phones, watches, and small unmanned aerial vehicles. The ...

2017

Generalized Pickands constants and stationary max-stable processes

Sebastian Engelke

Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, as such, their exact value is often unknown. Recently, D ...

Springer Verlag2017

Gaussian versus Sparse Stochastic Processes : Construction, Regularity, Compressibility

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

Stochastic partial differential equations driven by Lévy white noises : generalized random processes, random field solutions and regularity

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes

Adrian Blumenthal

Stochastic models that account for sudden, unforeseeable events play a crucial role in many different fields such as finance, economics, biology, chemistry, physics and so on. That kind of stochastic problems can be modeled by stochastic differential equat ...

EPFL2015

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

Fourier Analysis of Functional Time Series, with Applications to DNA Dynamics

Shahin Tavakoli

This work is about time series of functional data (functional time series), and consists of three main parts. In the first part (Chapter 2), we develop a doubly spectral decomposition for functional time series that generalizes the Karhunen–Loève expansion ...

EPFL2014

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

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

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

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

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

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization

Laura Vinckenbosch

The topic of this thesis is the study of several stochastic control problems motivated by sailing races. The goal is to minimize the travel time between two locations, by selecting the fastest route in face of randomly changing weather conditions, such as ...

EPFL2012

Stochastic integrals for spde's: A comparison

Robert Dalang

We present the Walsh theory of stochastic integrals with respect to martingale measures, and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of stochastic integrals with respect to Hilbert-space-valued Wiener processes, and ...

Elsevier2011

Ecohydrological Footprints : Quantitative Response of Ecosystems to Changes in their Hydrological Drivers

Samir Suweis

Ecohydrological footprints are defined as the response of ecosystem functions or services to changes in their hydrologic drivers. In this thesis, several diverse footprints are addressed: noise-driven effects on storage-discharge relations and catchment st ...

EPFL2011

On The Stochastic Modeling Of Rigid Body Systems With Application To Polymer Dynamics

John Maddocks

The stochastic equations of motion for a system of interacting rigid bodies in a solvent are formulated and studied. Three-dimensional bodies of arbitrary shape, with arbitrary couplings between translational and rotational degrees of freedom, as arise in ...

2010

Mean Field Asymptotic of Markov Decision Evolutionary Games and Teams

Jean-Yves Le Boudec

We introduce Markov Decision Evolutionary Games with N players, in which each individual in a large population interacts with other randomly selected players. The states and actions of each player in an interaction together determine the instantaneous payo ...

2009

The non-linear stochastic wave equation in high dimensions : existence, Hölder-continuity and Itô-Taylor expansion

Daniel Conus

The main topic of this thesis is the study of the non-linear stochastic wave equation in spatial dimension greater than 3 driven by spatially homogeneous Gaussian noise that is white in time. We are interested in questions of existence and uniqueness of so ...

EPFL2008