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Related publications (28)

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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 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

Filtration Shrinkage, Strict Local Martingales And The Follmer Measure

Martin Larsson

When a strict local martingale is projected onto a subfiltration to which it is not adapted, the local martingale property may be lost, and the finite variation part of the projection may have singular paths. This phenomenon has consequences for arbitrage ...

Inst Mathematical Statistics2014

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

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

On the rate of convergence in the martingale central limit theorem

Jean-Christophe Mourrat

Consider a discrete-time martingale, and let V-2 be its normalized quadratic variation. As V-2 approaches 1, and provided that some Lindeberg condition is satisfied, the distribution of the rescaled martingale approaches the Gaussian distribution. For any ...

Int Statistical Inst2013