Search results for "Probability"
showing 10 items of 3417 documents
Algorithmes Stochastiques
2010
National audience; Un algorithme stochastique est un outil d'optimisation particulièrement utile lorsque l'on observe les données "en ligne". Il permet, entre autres choses, d'estimer les paramètres de modèles statistiques avec des procédures généralement simples de mise à jour qui ne nécessitent pas la ré-estimation parfois très coûteuse en temps de calcul. Ces approches itératives possèdent de bonnes propriétés de convergence et atteignent même dans certains cas la vitesse optimale. Dans le vaste domaine d'applications, citons l'économie, la finance, la biologie, la physique mathématique, l'automatique, le traitement d'images jusqu'à la statistique non paramétrique. L'objet de cette sessi…
Some multivariate risk indicators ; estimation and application to optimal reserve allocation
2010
National audience; We consider a vectorial risk process ...
Algorithmes stochastiques et diffusions : l'étude par inégalités fonctionnelles
2010
National audience; Les algorithmes classiques que sont le recuit simulé ou l'algorithme de Robbins- Monro ont des équivalents en temps continu, qui sont des processus de diffusion non-homogènes.
CENTRAL LIMIT THEOREM FOR KERNEL ESTIMATOR OF INVARIANT DENSITY IN BIFURCATING MARKOV CHAINS MODELS
2021
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. Motivated by the functional estimation of the density of the invariant probability measure which appears as the asymptotic distribution of the trait, we prove the consistence and the Gaussian fluctuations for a kernel estimator of this density based on late generations. In this setting, it is interesting to note that the distinction of the three regimes on the ergodic rate identified in a previous work (for fluctuations of average over large generations) disappears. This result is a first step to go beyond the thresh…
CENTRAL LIMIT THEOREM FOR BIFURCATING MARKOV CHAINS
2020
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We first provide a central limit theorem for general additive functionals of BMC, and prove the existence of three regimes. This corresponds to a competition between the reproducing rate (each individual has two children) and the ergodicity rate for the evolution of the trait. This is in contrast with the work of Guyon (2007), where the considered additive functionals are sums of martingale increments, and only one regime appears. Our first result can be seen as a discrete time version, but with general trait evoluti…
Risk indicators with several lines of business: comparison, asymptotic behavior and applications to optimal reserve allocation
2013
International audience; In a multi-dimensional risk model with dependent lines of business, we propose to allocate capital with respect to the minimization of some risk indicators. These indicators are sums of expected penalties due to the insolvency of a branch while the global reserve is either positive or negative. Explicit formulas in the case of two branches are obtained for several models independent exponential, correlated Pareto). The asymptotic behavior (as the initial capital goes to infinity) is studied. For higher dimension and several periods, no explicit expression is available. Using a stochastic algorithm, we get estimations of the allocation, compare the different allocatio…
Cut-off method for endogeny of recursive tree processes
2016
Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process. We propose a new method of proving endogeny, which applies to various processes. As explicit examples, we establish endogeny of the random metrics on non-pivotal hierarchical graphs defined by multiplicative cascades and of mean-field optimization problems as the mean-field matching and travelling salesman problems in pseudo-dimension q>1.
Exploring the Solar Wind from Its Source on the Corona into the Inner Heliosphere during the First Solar Orbiter-Parker Solar Probe Quadrature
2021
This Letter addresses the first Solar Orbiter (SO) -- Parker Solar Probe (PSP) quadrature, occurring on January 18, 2021, to investigate the evolution of solar wind from the extended corona to the inner heliosphere. Assuming ballistic propagation, the same plasma volume observed remotely in corona at altitudes between 3.5 and 6.3 solar radii above the solar limb with the Metis coronagraph on SO can be tracked to PSP, orbiting at 0.1 au, thus allowing the local properties of the solar wind to be linked to the coronal source region from where it originated. Thanks to the close approach of PSP to the Sun and the simultaneous Metis observation of the solar corona, the flow-aligned magnetic fiel…
Geometric Optimal Control of Simple Quantum Systems
2011
International audience
Weak Langmuir turbulence in disordered multimode optical fibers
2021
We consider the propagation of temporally incoherent waves in multimode optical fibers (MMFs) in the framework of the multimode nonlinear Schr\"odinger (NLS) equation accounting for the impact of the natural structural disorder that affects light propagation in standard MMFs (random mode coupling and polarization fluctuations). By averaging the dynamics over the fast disordered fluctuations, we derive a Manakov equation from the multimode NLS equation, which reveals that the Raman effect introduces a previously unrecognized nonlinear coupling among the modes. Applying the wave turbulence theory on the Manakov equation, we derive a very simple scalar kinetic equation describing the evolution…