Search results for " Probability"
showing 10 items of 2176 documents
Solving chance constrained optimal control problems in aerospace via Kernel Density Estimation
2017
International audience; The goal of this paper is to show how non-parametric statistics can be used to solve some chance constrained optimization and optimal control problems. We use the Kernel Density Estimation method to approximate the probability density function of a random variable with unknown distribution , from a relatively small sample. We then show how this technique can be applied and implemented for a class of problems including the God-dard problem and the trajectory optimization of an Ariane 5-like launcher.
Fractal Weyl law for open quantum chaotic maps
2014
We study the semiclassical quantization of Poincar\'e maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result encompasses the case of several convex (hard) obstacles satisfying a no-eclipse condition.
Automated uncertainty quantification analysis using a system model and data
2015
International audience; Understanding the sources of, and quantifying the magnitude of, uncertainty can improve decision-making and, thereby, make manufacturing systems more efficient. Achieving this goal requires knowledge in two separate domains: data science and manufacturing. In this paper, we focus on quantifying uncertainty, usually called uncertainty quantification (UQ). More specifically, we propose a methodology to perform UQ automatically using Bayesian networks (BN) constructed from three types of sources: a descriptive system model, physics-based mathematical models, and data. The system model is a high-level model describing the system and its parameters; we develop this model …
Study and Comparison of Surface Roughness Measurements
2014
Journées du Groupe de Travail en Modélisation Géométrique (GTMG'14), Lyon; This survey paper focus on recent researches whose goal is to optimize treatments on 3D meshes, thanks to a study of their surface features, and more precisely their roughness and saliency. Applications like watermarking or lossy compression can benefit from a precise roughness detection, to better hide the watermarks or quantize coarsely these areas, without altering visually the shape. Despite investigations on scale dependence leading to multi-scale approaches, an accurate roughness or pattern characterization is still lacking, but challenging for those treatments. We think there is still room for investigations t…
Statistics of transitions for Markov chains with periodic forcing
2013
The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In particular the first Floquet multiplier of the associated generating function can be explicitly computed and related to the equilibrium probability measure of an associated process in higher dimension. An application to the stochastic resonance is presented.
PARAMETER ESTIMATION FOR FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES: NON-ERGODIC CASE
2011
We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index $H\in(1/2,1)$. We study the consistency and the asymptotic distributions of the least squares estimator $\hat{\theta}_t$ of $\theta$ based on the observation $\{X_s,\ s\in[0,t]\}$ as $t\rightarrow\infty$.
Exact simulation of diffusion first exit times: algorithm acceleration
2020
In order to describe or estimate different quantities related to a specific random variable, it is of prime interest to numerically generate such a variate. In specific situations, the exact generation of random variables might be either momentarily unavailable or too expensive in terms of computation time. It therefore needs to be replaced by an approximation procedure. As was previously the case, the ambitious exact simulation of exit times for diffusion processes was unreachable though it concerns many applications in different fields like mathematical finance, neuroscience or reliability. The usual way to describe exit times was to use discretization schemes, that are of course approxim…
Variable Length Markov Chains, Persistent Random Walks: a close encounter
2020
This is the story of the encounter between two worlds: the world of random walks and the world of Variable Length Markov Chains (VLMC). The meeting point turns around the semi-Markov property of underlying processes.
Statistical consequences of the Devroye inequality for processes. Applications to a class of non-uniformly hyperbolic dynamical systems
2005
In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functio…
Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes *
2013
A classical random walk $(S_t, t\in\mathbb{N})$ is defined by $S_t:=\displaystyle\sum_{n=0}^t X_n$, where $(X_n)$ are i.i.d. When the increments $(X_n)_{n\in\mathbb{N}}$ are a one-order Markov chain, a short memory is introduced in the dynamics of $(S_t)$. This so-called "persistent" random walk is nolonger Markovian and, under suitable conditions, the rescaled process converges towards the integrated telegraph noise (ITN) as the time-scale and space-scale parameters tend to zero (see Herrmann and Vallois, 2010; Tapiero-Vallois, Tapiero-Vallois2}). The ITN process is effectively non-Markovian too. The aim is to consider persistent random walks $(S_t)$ whose increments are Markov chains with…