Search results for "Stochastic algorithm"

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Approximation of exit times for one-dimensional linear diffusion processes

2020

International audience; In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and the Ornstein-Uhlenbeck context, that is for particular time-homogeneous diffusion processes. Here the aim is therefore to generalize this efficient numerical approach in order to obtain an approximation of both the exit time and position for a general linear diffusion. The main challenge of such a generalization is to handle with time-inhomogeneous diffusions. The efficiency of the method is described with particular care through theoretical results and numerical example…

GeneralizationOrder (ring theory)Context (language use)Exit timeRandom walk010103 numerical & computational mathematicsStochastic algorithmRandom walk01 natural sciencesLinear diffusion010101 applied mathematicsComputational MathematicsComputational Theory and MathematicsDiffusion processPosition (vector)Modeling and SimulationApplied mathematicsGeneralized spheroids[MATH]Mathematics [math]0101 mathematicsDiffusion (business)Brownian motionMathematicsComputers & Mathematics with Applications
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Stochastic algorithms for robust statistics in high dimension

2016

This thesis focus on stochastic algorithms in high dimension as well as their application in robust statistics. In what follows, the expression high dimension may be used when the the size of the studied sample is large or when the variables we consider take values in high dimensional spaces (not necessarily finite). In order to analyze these kind of data, it can be interesting to consider algorithms which are fast, which do not need to store all the data, and which allow to update easily the estimates. In large sample of high dimensional data, outliers detection is often complicated. Nevertheless, these outliers, even if they are not many, can strongly disturb simple indicators like the me…

Stochastic AlgorithmsAlgorithmes StochastiquesAlgorithmes RécursifsRecursive AlgorithmsStatistique RobusteAlgorithmes de Gradient StochastiquesAveragingStochastic Gradient AlgorithmsMoyennisationGrande DimensionRobust StatisticsFunctional DataDonnées Fonctionnelles[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]Geometric MedianHigh DimensionMédiane Géométrique
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