We reproduce here two texts from Marc Yor, parts of his “testament scientifique” in relation with enlargement of filtration. The full version of these texts can be found on http://www.math-evry.cnrs.fr/pmf/marc_yor/publication?.
From the presentation of T. Jeulin, on May 3rd 2016 at Institut Henri Poincaré, Paris.D'après les notes d'exposé de T. Jeulin du 3 mai 2016 à Paris, Institut Henri Poincaré.
When the martingale representation property holds, we call any local martingale which realizes the representation a representation process. There are two properties of the representation process which can greatly facilitate the computations under the martingale representation property. On the one hand, the representation process is not unique and there always exists a...
In this paper, we are interested by advanced backward stochastic differential equations (ABSDEs), in a probability space equipped with a Brownian motion and a single jump process, with a jump at time τ. ABSDEs are BSDEs where the driver depends on the future paths of the solution. We show, that under immersion hypothesis between the Brownian filtration and its progressive...
We consider trading against a hedge fund or large trader that must liquidate a large position in a risky asset if the market price of the asset crosses a certain threshold. Liquidation occurs in a disorderly manner and negatively impacts the market price of the asset. We consider the perspective of small investors whose trades do not induce market impact and who possess different...
The occurrence of some events can impact asset prices and produce losses. The amplitude of these losses are partly determined by the degree of predictability of those events by the market investors, as risk premiums build up in an asset price as a compensation of the anticipated losses. The aim of this paper is to propose a general framework where these phenomena can be properly...
Workshop on low velocity flows: contributions
This article presents different recent theoretical results illustrating the interactions between probability and algorithmics. These contributions deal with various topics: cellular automata and calculability, variable length Markov chains and persistent random walks, perfect sampling via coupling from the past. All of them involve discrete dynamics on complex random structures...
The paper is devoted to some new results concerning the topology of hyperspaces of max-plus convex subsets in Euclidean spaces and some other spaces.RésuméL’article est dévoué à de nouveaux résultats concernant la topologie de hyperespaces de sous-ensembles max-plus convexes dans des espaces euclidiens et d’autres espaces.
This paper is devoted to non-cooperative games in idempotent measures. We consider two kinds of such games. Firstly, players are allowed to play their mixed idempotent strategies. We also consider games where belief of each player about a choice of the strategy by the other players is an idempotent measure. We prove existence of equilibria in both cases and discuss the difference...
We present in this work a system for unidimensional granular flows first mentioned in a paper of A. Lefebvre–Lepot and B. Maury (2011), which captures the transitions between compressible and incompressible phases. This model exhibits in the incompressible regions some memory effects through an additional variable called adhesion potential. We derive this system from compressible...
We consider multivariate time series that exhibit reduced rank cointegration, which means a lower dimensional linear projection of the process becomes stationary. We will review recent suitable Markov Chain Monte Carlo approaches for Bayesian inference such as the Gibbs sampler of [41] and the Geodesic Hamiltonian Monte Carlo method of [3]. Then we will propose extensions that...
We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse non-parametric estimation in multivariate Gaussian regression model. It rests on the construction of a metamodel for aproximating the Hoeffding-Sobol...
Considered here is repeated interaction among economic agents. These must share privately held user rights to diverse production factors. The disparate features of the resulting economy motivate a solution concept which blends Cournot/Nash equilibrium with that of Walras. A novelty comes by showing that integrated equilibrium may emerge via adaptive behavior and repeated play.
We propose a method to explain the behaviour of the Godunov finite volume scheme applied to the linear wave equation with Coriolis source term at low Froude number. In particular, we use the Hodge decomposition and we study the properties of the modified equation associated to the Godunov scheme. Based on the structure of the discrete kernel of the linear operator discretized by...
Automatic differentiation has been involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic differentiation can be used. In between formal derivation and standard numerical schemes, this approach is based on software solutions applying...
Breiman's (2001) random forests are a very popular class of learning algorithms often able to produce good predictions even in high-dimensional frameworks, with no need to accurately tune its inner parameters. Unfortunately, there are no theoretical findings to support the default values used for these parameters in Breiman's algorithm. The aim of this paper is therefore to...
We introduce a mixture model intended to describe the dynamics of the mucus layer that wraps the gut mucosa. This model takes into account the fluid mechanics of the gut content, the inhomogeneous rheology that depends on the fluid composition, and the main physiological mechanisms that ensure the homoeostasis of the mucus layer. Numerical simulations, based on a finite volume...
The aim of this project is to validate the Vivabrain pipeline with a physical phantom from real MRI acquisition to MRI simulations through image segmentation and computational fluid dynamics (CFD) simulations. For that purpose, we set up three comparison benchmarks. The first benchmark compares dimensions of the reconstructed geometry from real MRI acquisition to the physical...
We are interested in this paper in the modelling and numerical simulation of some phenomena that are observed in the context of car dynamics, in particular the appearance of persistent jams upstream critical points with no real cause of flux limitation. We shall consider the case of a stable jam on a freeway upstream an accident that took place on the opposite lane. This...
In this paper, we propose a mathematical model to describe the functioning of a bioreactor landfill, that is a waste management facility in which biodegradable waste is used to generate methane. The simulation of a bioreactor landfill is a very complex multiphysics problem in which bacteria catalyze a chemical reaction that starting from organic carbon leads to the production of...
This paper deals with the numerical treatment of two additional terms in the Lmnc-system modelling the coolant in a nuclear reactor core. The latter model was derived and studied by the authors in previous publications. On the one hand, we investigate the influence of the thermal conduction upon steady analytical solutions and upon numerical strategies designed in dimensions 1...