Showing papers in "Esaim: Proceedings in 2014"
TL;DR: A short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs) and a short overview on numerical methods used for simulating PDMPs.
Abstract: We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases such as the TCP model or a model of switched vector fields, better results can be proved, especially as regards long time behaviour. We continue our review with an infinite dimensional example of neuronal activity. From the statistical point of view, these models provide specific challenges: we illustrate this point with the example of the estimation of the distribution of the inter-jumping times. We conclude with a short overview on numerical methods used for simulating PDMPs.
68 citations
TL;DR: In this article, a selective review on probabilistic modeling of heterogeneity in random graphs is presented, focusing on latent space models and more particularly on stochastic block models and their extensions that have undergone major developments in the last five years.
Abstract: We present a selective review on probabilistic modeling of heterogeneity in random graphs. We focus on latent space models and more particularly on stochastic block models and their extensions that have undergone major developments in the last five years.
67 citations
TL;DR: In this article, a pedagogical introduction to the stochastic modeling and theoretical analysis of interacting particle algorithms is provided, as well as several applications including random walk confinements, particle absorption models, nonlinear filtering, stochiastic optimization, combinatorial counting and directed polymer models.
Abstract: Interacting particle methods are increasingly used to sample from complex high-dimensional distributions. They have found a wide range of applications in applied probability, Bayesian statistics and information engineering. Understanding rigorously these new Monte Carlo simulation tools leads to fascinating mathematics related to Feynman-Kac path integral theory and their interacting particle interpretations. In these lecture notes, we provide a pedagogical introduction to the stochastic modeling and the theoretical analysis of these particle algorithms. We also illustrate these methods through several applications including random walk confinements, particle absorption models, nonlinear filtering, stochastic optimization, combinatorial counting and directed polymer models.
55 citations
TL;DR: In this article, the local well-posedness of two types of generalized kinetic Cucker-Smale (in short C-S) equations was studied, where singularities are present either in space or in velocity.
Abstract: In this paper, we study the local well-posedness of two types of generalized kinetic Cucker-Smale (in short C-S) equations. We consider two different communication weights in space with nonlinear coupling of the velocities, v | v | β − 2 for β > 3-d/2, where singularities are present either in space or in velocity. For the singular communication weight in space, ψ 1 (x ) = 1 / | x | α with α ∈ (0,d − 1), d ≥ 1, we consider smooth velocity coupling, β ≥ 2. For the regular one, we assume ψ2 (x) ∈ (Lloc ∞ ∩ Liploc ) (Rd ) but with a singular velocity coupling β ∈ (3-d/2, 2). We also present the various dynamics of the generalized C-S particle system with the communication weights ψ i ,i = 1,2 when β ∈ (0,3). We provide sufficient conditions of the initial data depending on the exponent β leading to finite-time alignment or to no collisions between particles in finite time.
38 citations
TL;DR: In this article, the authors present several aspects of concentration phenomena in high dimensional geometry, including a geometric analysis point of view coming from the theory of high dimensional convex bodies, which has a broad audience going from algorithmic convex geometry to random matrices.
Abstract: The purpose of this note is to present several aspects of concentration phenomena in high dimensional geometry. At the heart of the study is a geometric analysis point of view coming from the theory of high dimensional convex bodies. The topic has a broad audience going from algorithmic convex geometry to random matrices. We have tried to emphasize dierent problems relating these areas of research. Another connected area is the study of probability in Banach spaces where some concentration phenomena are related with good comparisons between the weak and the strong moments of a random vector. Resume. Le but de cette note est de presenter plusieurs aspects du phenomene de concentration en geometrie de grande dimension. Au cœur de l'etude figure un point de vue d'analyse geometrique provenant de la theorie des corps convexes en grande dimension. Ce theme a une large audience, allant de la geometrie convexe algorithmique a la theorie des matrices aleatoires. Nous avons tente de mettre en avant les divers problemes reliant les dierents
26 citations
TL;DR: A short survey of recent findings concerning normal approximations on a Gaussian space can be found in this article, where Stein's method, Poincare-type inequalities, as well as the use of techniques from information theory are discussed.
Abstract: I will provide a short survey of recent findings concerning normal approximations on a Gaussian space. The results discussed in this work involve Stein's method, Poincare-type inequalities, as well as the use of techniques from information theory. The guiding example involves 'exploding Brownian functionals', that are used as a tool for enhancing the reader's intuition.
17 citations
TL;DR: The martingale optimal transport problem as mentioned in this paper provides a systematic framework for the robust hedging problem and, therefore, allows to derive sharp Martingale inequalities independently of any reference probability measure on the paths space.
Abstract: In the recent literature, martingale inequalities have been emphasized to be induced by pathwise inequalities independently of any reference probability measure on the paths space. This feature is closely related to the problem of robust hedging in nancial mathematics, which was originally addressed in some specic cases by means of the Skorohod embedding problem. The martingale optimal transport problem provides a systematic framework for the robust hedging problem and, therefore, allows to derive sharp martingale inequalities. We illustrate this methodology by deriving the sharpest possible control of the running maximum of a martingale by means of a nite number of marginals.
16 citations
TL;DR: Several state-of-the-art Monte Carlo methods for simulating and estimating rare events, motivated by theoretical issues as well as by applied problems are presented.
Abstract: This article presents several state-of-the-art Monte Carlo methods for simulating and estimating rare events. A rare event occurs with a very small probability, but its occurrence is important enough to justify an accurate study. Rare event simulation calls for specific techniques to speed up standard Monte Carlo sampling, which requires unacceptably large sample sizes to observe the event a sucient number of times. Among these variance reduction methods, the most prominent ones are Importance Sampling (IS) and Multilevel Splitting, also known as Subset Simulation. This paper oers some recent results on both aspects, motivated by theoretical issues as well as by applied problems. Resume. Cet article propose un etat de l'art de plusieurs methodes Monte Carlo pour l'estimation d'evenements rares. Un evenement rare est par definition un evenement de probabilite tres faible, mais d'importance pratique cruciale, ce qui justifie une etude precise. La methode Monte Carlo classique s'averant prohibitivement couteuse, il importe d'appliquer des techniques specifiques pour leur estima- tion. Celles-ci se divisent en deux grandes categories : echantillonnage preferentiel d'un cote, methodes multi-niveaux de l'autre. Nous presentons ici quelques resultats recents dans ces domaines, motives par des considerations tant pratiques que theoriques.
16 citations
TL;DR: This overview presents recent results since the introduction of approximate Bayesian computation techniques about ten years ago in population genetics.
Abstract: Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics. Resume. Les methodes bayesiennes approchees constituent l'un des outils majeurs d'inference statis- tique en dimension finie lorsque la vraisemblance du modele parametrique considere n'est pas accessible. Nous presentons quelques resultats recents qui ont permis d'augmenter significativement l'ecacite de
15 citations
TL;DR: In this article, the authors present and discuss the situ- ations in which this equilibrium prole can be explicitly found, and apply it to dissipative gases and to wealth redistribution models.
Abstract: Bilinear kinetic models of Maxwell-Boltzmann type are often used to model socio-economic systems composed by agents that undergo binary interactions, which in general obey to some conserva- tion law. Then, the details of the microscopic interaction are such that an equilibrium solution emerges. At dierence with the classical Boltzmann equation for elastic gas particles, the analytic form of the equilibria is known only in some particular case. In the present note, we present and discuss the situ- ations in which this equilibrium prole can be explicitly found. Applications to dissipative gases and to wealth redistribution models are presented.
14 citations
TL;DR: In this article, the existence and regularity of minimizers to shape optimization problems were investigated. But the mathematical questions concerning the existence of the minimizers and their regularity still remain open.
Abstract: In 1973, Helfrich suggested a simple model to describe the shapes of vesicles: a free bending energy involving geometric quantities like curvature. However, the mathematical questions concerning the existence and the regularity of minimizers to such shape optimization problems still remain open. In this article, we consider a class of admissible shapes in which the existence of minimizers is ensured: the hypersurfaces of R n satisfying a uniform ball condition. We prove that this property is equivalent to the notion of positive reach introduced by Federer in 1959. Then, another characterization in terms of C 1,1 -regularity is established for compact hypersurfaces.
TL;DR: These notes correspond to a three hours lecture given during the workshop "Metastability and Stochastic Processes" held in Marne la Vall as mentioned in this paper, which was held in 2003.
Abstract: These notes correspond to a three hours lecture given during the workshop \Metastability and Stochastic Processes" held in Marne la Vall
TL;DR: In this paper, an analytical approximation of the forward implied volatility with a precise error estimate is proposed to efficiently price forward start options in time-dependent local volatility models as the forward start date, the maturity or the volatility coefficient are small.
Abstract: We introduce an analytical approximation to efficiently price f orward start options on eq- uity in time-dependent local volatility models as the forward start date, the maturity or the volatility coefficient are small. We use a conditional expectation argument to represent the price as an expecta- tion of a Black-Scholes formula computed with a stochastic implied volatility depending on the value of the equity at the forward date. Then we perform a volatility expansion to derive an analytical approximation of the forward implied volatility with a precise error estimate. We also illustrate the accuracy of the formula with some numerical experiments. Some results and tools of this work were presented at the conference SMAI 2013 in the mini-symposium "Methodes asymptotiques en finance". Resume. Nous introduisons une approximation analytique afin d'´evaluer efficacement les options ` depart differe dites forward start dans les modelesvolatilite locale qui depend du temps quand la date forward, la maturite ou le coefficient de volatilite sont petits. Nous utilisons un argument d'esperance conditionnelle pour representer le prix comme l'esperance d'une formule de Black-Scholes calculee avec une volatilite implicite stochastique qui depend de la valeur de l'actionla date forward. Ensuite, nous effectuons un developpement en volatilite pour obtenir une approximation analytique de la volatilite implicite forward avec une estimation precise de l'erreur. Nous illustronsla precision de notre formule avec quelques experiences numeriques. Certains resultats et outils de ce travail onte presentes au congres SMAI 2013 dans le mini-symposium "Methodes asymptotiques en finance".
TL;DR: A fictitious domain method for the Stokes problem which allows computations in domains whose boundaries do not depend on the mesh, based on the ideas of Xfem and first introduced for the Poisson problem.
Abstract: In this work we develop a ctitious domain method for the Stokes problem which allows computations in domains whose boundaries do not depend on the mesh. The method is based on the ideas of Xfem and has been rst introduced for the Poisson problem. The uid part is treated by a mixed nite element method, and a Dirichlet condition is imposed by a Lagrange multiplier on an immersed structure localized by a level-set function. A stabilization technique is carried out in order to get the convergence for this multiplier. The latter represents the forces that the uid applies on the structure. The aim is to perform uid-structure simulations for which these forces have a central role. We illustrate the capacities of the method by extending it to the incompressible Navier-Stokes equations coupled with a moving rigid solid.
TL;DR: Possible research routes to be explored in order to make progress on networks with many short loops, involving old and new random graph models and ideas for novel mathematical methods are sketched.
Abstract: Networks observed in the real world often have many short loops. This violates the tree- like assumption that underpins the majority of random graph models and most of the methods used for their analysis. In this paper we sketch possible research routes to be explored in order to make progress on networks with many short loops, involving old and new random graph models and ideas for novel mathematical methods. We do not present conclusive solutions of problems, but aim to encourage and stimulate new activity and in what we believe to be an important but under-exposed area of research. We discuss in more detail the Strauss model, which can be seen as the 'harmonic oscillator' of 'loopy' random graphs, and a recent exactly solvable immunological model that involves random graphs with extensively many cliques and short loops. Resume. Les reseaux observes dans la Nature ont souvent des cycles courts. Ceci contredit le postulat de hierarchie sur lequel se base la majorite des modeles de reseaux aleatoires et la plupart des methodes utilisees pour leur analyse. Dans cet article, nous esquissons des directions de recherches possibles, afin de progresser sur les reseaux contenant beaucoup de cycles courts, faisant appel a des modeles de reseaux aleatoires eprouves ou nouveaux, et des idees pour de nouvelles methodes mathematiques. Nous ne presentons pas de solutions definitives, mais notre but est d'encourager et de stimuler de nouveaux travaux dans ce que nous croyons etre une direction de recherche importante, bien que insusamment exploree. Nous discutons en detail le modele de Strauss, qui peut etre considere comme 'l'oscillateur harmonique' des reseaux aleatoires 'a boucles', ainsi qu'un modele immunologique soluble exactement qui comporte des reseaux aleatoires avec de nombreux cliques et cycles courts.
TL;DR: In this article, an easy approach based on a classical construction by Dacorogna and Moser is described to prove that optimal vector fields in some minimal flow problem linked to optimal transport models are induced by a probability measure on the space of paths.
Abstract: The papers describes an easy approach, based on a classical construction by Dacorogna and Moser, to prove that optimal vector fields in some minimal flow problem linked to optimal transport models (congested traffic, branched transport, Beckmann's problem...) are induced by a probability measure on the space of paths. This gives a new, easier, proof of a classical result by Smirnov, and allows handling optimal flows without taking care of the presence of cycles. Resume. Cet article presente une approche simple, basee sur une construction classique de Dacorogna et Moser, pour montrer que les champs de vecteurs optimaux dans certains problemes de flot minimal lies a des modeles de transport (trafic congestionne, transport branche, probleme de Beckmann...) sont induits par des mesures de probabilite sur l'espace des chemins. Cela donne aussi une preuve nouvelle et plus simple d'un resultat classique de Smirnov, et permet de traiter les flots optimaux sans se preoccuper de la presence eventuelle de cycles.
TL;DR: Self-reproducing systems represent ensemble of objects which can produce other objects similar to themselves, and the aggregates correspond to biological populations, and emergence of new aggregates to the process of speciation.
Abstract: Self-reproducing systems (SRS) represent ensemble of objects (or individuals) which can produce other objects similar to themselves. If they compete with each other for resources, then they can form aggregates (or clusters) instead of a uniform distribution. New aggregates can split from the previous ones. In terms of biological populations, the aggregates correspond to biological species, and emergence of new aggregates to the process of speciation. Other examples of SRS will also be discussed.
TL;DR: A new mechanism for undersampling chaotic numbers obtained by the ring coupling of one-dimensional maps is proposed which allows the building of a PRNG which passes all NIST Test.
Abstract: We propose a new mechanism for undersampling chaotic numbers obtained by the ring coupling of one-dimensional maps. In the case of 2 coupled maps this mechanism allows the building of a PRNG which passes all NIST Test. This new geometric undersampling is very eective for generating 2 parallel streams of pseudo-random numbers, as we show, computing carefully their properties, up to sequences of 10 12 consecutives iterates of the ring coupled mapping which provides more than 3:35 10 10
TL;DR: This paper presents how three classic approaches in computer arithmetic may provide some first steps towards more numerical reproducibility.
Abstract: Questions whether numerical simulation is reproducible or not have been reported in several sensitive applications. Numerical reproducibility failure mainly comes from the finite precision of computer arithmetic. Results of floating-point computation depends on the computer arithmetic precision and on the order of arithmetic operations. Massive parallel HPC which merges, for instance, many-core CPU and GPU, clearly modifies these two parameters even from run to run on a given computing platform. How to trust such computed results? This paper presents how three classic approaches in computer arithmetic may provide some first steps towards more numerical reproducibility.
TL;DR: In this paper, a series of recent works related to some multiscale problems motivated by practical problems in Mechanics are presented, and a special emphasis is laid on situations where the amount of randomness is small, or when the disorder is limited.
Abstract: We overview a series of recent works related to some multiscale problems motivated by practical problems in Mechanics. The common denominator of all these works is that they address multiscale problems where the geometry of the microstructures is not periodic. Random modelling, as well as other types of nonperiodic modelling, can then be used to account for the imperfections of the medium. The theory at play is that of homogenization, in its many variants (stochastic, general deterministic, periodic). The numerical methods developed and adapted are finite element type methods. A special emphasis is laid on situations where the amount of randomness is small, or, put differently, when the disorder is limited. Then, specific, computationally efficient techniques can be designed and employed.
TL;DR: In this article, a time integration method for the resolution of ordinary and partial dierential equations is proposed, which consists in computing a formal solution as a (eventually divergent) time series.
Abstract: A time integration method for the resolution of ordinary and partial dierential equations is proposed. The method consists in computing a formal solution as a (eventually divergent) time series. Next, the Borel resummation method is applied to deduce an (sectorial) analytical solution. The speed and spectral properties of the scheme are analyzed through some examples. Applications to fluid mechanics are presented. ResumOn propose une methode numerique d'integration temporelle d'´ equations di´ erentielles ou aux derivees partielles. Cette methode consiste d'abordcalculer une solution sous forme de serie formelle, dont le rayon de convergence peutnul. Ensuite, la methode de resommation de Borel- Laplace est utilisee pour deduire une solution analytique (dans un secteur) de l'´ equation. La rapidite et les proprietes geometriques du schema sont analyseestravers quelques exemples. Des applications en mecanique des fluides sont presentees.
TL;DR: In this article, a simplified model describing the evolution of the coolant within a nuclear reactor core (e.g. of PWR type) is investigated. But the model is based on the Finite Element software FreeFem++.
Abstract: We investigate a simplified model describing the evolution of the coolant within a nuclear reactor core (e.g. of PWR type). This model is named LMNC (for Low Mach Nuclear Core) and consists of the coupling between three equations of different types together with boundary conditions specific to the nuclear framework. After several articles dedicated to dimension 1, we present in this paper some monophasic two-dimensional numerical results when the fluid is modelled by the stiffened gas law describing the pure liquid phase. The underlying numerical strategy is based on the Finite-Element software FreeFem++.
TL;DR: In this article, a low-order absorbing boundary condition (ABC) for 2D elliptic TTI media, preserving the system stability, was constructed based on comparing and then connecting the slowness curves for isotropic and elliptic tTI waves.
Abstract: This work deals with the construction of a low-order absorbing boundary condition (ABC) for 2D elliptic TTI media, preserving the system stability. The construction is based on comparing and then connecting the slowness curves for isotropic and elliptic TTI waves. Numerical experiments illustrate the performance of the new ABC. They are performed by integrating the ABC in a DG formulation of Elastodynamics. When applied in a TTI medium, the new ABC performs well with the same level of accuracy than the standard isotropic ABC set in an isotropic medium. The condition demonstrates also a good robustness when applied for large times of simulation.
TL;DR: In this paper, the authors present a survey of related topics concerning the embeddability of given mappings in real manifolds, focusing on the relationship between the problem of the embed-dability and functional equations.
Abstract: This is a survey paper on selected topics concerning the embeddability of given mappings in real ows. Particular attention will be paid to the relationship between the problem of the embed- dability and functional equations. Let X be a real manifold and f : X! X be a homeomorphism. A family of homeomorphismsff t : X ! X;t2 Rg such that f t f s = f t+s for t;s2 R and f 1 = f is said to be an embedding of f. The embedding is of class C r if for every x2 X the mapping t! f t (x) is continuous and all f t are of class C r . We concentrate on the cases where X is an open subset of R N ; X is a closed and an open interval, and X is a circle. We discuss the following problems: the existence of embeddings with suitable regularity; the conditions which imply the uniqueness of embeddings; the formulas expressing the above embeddings or their general constructions. R esum
TL;DR: A rough survey of results on iterative roots (fractional iterates) can be found in this article, where the main topics are: the conjugacy of piecewise monotonic functions and their iterative root, stability of iterative Root, some substitutes and generalizations of the notion of Iterative Root using set-valued functions.
Abstract: This is a rough survey of some results on iterative roots (fractional iterates) published recently. Also some historical information to clear the connection to previous results has been given. The main topics are: the conjugacy of piecewise monotonic functions and their iterative roots, stability of iterative roots, some substitutes and generalizations of the notion of iterative root using set-valued functions.
TL;DR: In this paper, a general approach to shape deformation analysis, using the framework of optimal control theory, is proposed. But this point of view can be made independent from the parametrization of the shape, and allows to model general constrained shape analysis problems.
Abstract: Shape deformation analysis is concerned with determining a deformation of a given shape into another one, which is optimal for a certain cost. We provide the main ideas for a new general approach to shape deformation analysis, using the framework of optimal control theory. This point of view can be made independent from the parametrization of the shape, and allows to model general constrained shape analysis problems. The use of a infinite dimensional variant of the con-strained Pontryagin Maximum Principle characterizes the optimal solutions of the shape deformation problem in a very general way. Resume. L'analyse des deformations consiste a determiner une transformation d'une forme donnee en une autre, optimale pour un certain cout. Nous donnons ici les idees principales pour une nouvelle approche generale pour cette analyse a l'aide de la theorie du controle optimal. Ce point de vue peu etre pris demani ere a ne pas dependre de la parametrisation de la forme, et perme egalement de modeliser des contraintes dans lesprobi emes d'analyse de deformations. Nous utilisons une variante en dimension infinie (cadre naturel de l'analyse des deformations) du principe du maximum de Pontryagin avec contraintes permettant de caracteriser de facont es generale les deformations optimales recherchees.
TL;DR: This work proposes an efficient finite volume approximation of twofluid flows using a faster relaxation Riemann solver and applies Strang directional splitting and optimized memory transpositions in order to achieve high performance on Graphics Processing Unit (GPU) or GPU cluster computations.
Abstract: In this work we propose an efficient finite volume approximation of twofluid flows. Our scheme is based on three ingredients. We first construct a conservative scheme that removes the pressure oscillations phenomenon at the interface. The construction relies on a random sampling at the interface [6, 5]. Secondly, we replace the exact Riemann solver by a faster relaxation Riemann solver with good stability properties [4]. Finally, we apply Strang directional splitting and optimized memory transpositions in order to achieve high performance on Graphics Processing Unit (GPU) or GPU cluster computations.
TL;DR: In this article, a review of existing concentration inequalities for counting processes is presented, with a focus on adaptive statistics for counting process counting, which need particular concentration inequalities to define and calibrate the methods as well as to precise the theoretical performance of the statistical inference.
Abstract: Adaptive statistics for counting processes need particular concentration inequalities to define and calibrate the methods as well as to precise the theoretical performance of the statistical inference. The present article is a small (non exhaustive) review of existing concentration inequalities that are useful in this context. Resume. Les statistiques adaptatives pour les processus de comptage necessitent des inegalites de concentration particulieres pour definir et calibrer les methodes ainsi que pour comprendre les perfor- mances de l'inference statistique. Cet article est une revue non exhaustive des inegalites de concentra- tion qui sont utiles dans ce contexte.
TL;DR: This paper presents three-dimensional numerical simulations of electromagnetic waves solved by the Discontinuous Galerkin (DG) method and exploits two levels of parallelism for achieving high performance.
Abstract: In this paper we present three-dimensional numerical simulations of electromagnetic waves. The Maxwell equations are solved by the Discontinuous Galerkin (DG) method. For achieving high performance, we exploit two levels of parallelism. The coarse grain parallelism is managed through MPI and a classical domain decomposition. The fine grain parallelism is managed with OpenCL in order to optimize the local computations on multicore processors or GPU's. We present several numerical experiments and performance comparisons. Resume. Dans cet article, nous presentons des simulations numeriques tridimensionnelles d'ondes electromagnetiques. Les equations de Maxwell sont resolues par la methode de Galerkin Discontinue (GD). Pour accelerer les calculs, nous exploitons deux niveaux de parallelisme. Le large grain est base sur MPI. Le parallelisme a grain fin repose sur OpenCL afin d'exploiter les processeurs massivement multicoeur (GPU ou CPU) recents. Nous presentons plusieurs experiences numeriques et des tests de performance.
TL;DR: In this article, the authors improve the continuous-in-time financial model developed in Frenod & Chakkour (2), that describes working of loan and repayment, in order to prepare its capability to be used in control theory approach.
Abstract: The achievement of a project requires tools to monitor and adjust its evolution over time. Rather than to check at mid-term whether the objectives will be achieved or not, and adjust them, it is interesting to develop a control tool in order to eectively conduct the project's objectives. In this paper, we improve the continuous-in-time financial model developed in Frenod & Chakkour (2), that describes working of loan and repayment, in order to prepare its capability to be used in control theory approach. The aim of this study is to determine the optimal loan schedule taking into account the objective of the project, the income and the spending. For that, we set out an optimal control method for the strategy elaboration phase to better adjust the project implementation. Resume. La realisation d'un projet necessite des outils pour surveiller et ajuster son evolution au fil du temps. Plutot que de verifier a mi-parcours si les objectifs seront atteints ou non, et les adapter, il est interessant de developper un outil de controle afin de mener ecacement les objectifs du projet. Dans cet article nous adaptons le modele financier continu en temps, developpe par Frenod & Chakkour (2) et qui decrit la facon d'emprunter et de rembourser, afin de l'utiliser dans le cadre de la theorie de controle. Le but c'est de determiner la strategie d'emprunt optimal pour atteindre les objectifs d'un projet. Cette strategie doit tenir compte du delai du projet, du taux d'interet de l'emprunt, des recettes et des depenses courantes. Une fois cette strategie est etablie, et tout au long du deroulement du projet, il est indispensable de controler la facon dont le plan de l'emprunt est implemente. Pour cela, nous avons mis en place une methode de controle optimal de la phase d'elaboration de la strategie, afin de mieux ajuster la mise en œuvre de l'implementation du projet.