CAMPILLO , Fabien

We study an approximation method for the one-dimensional nonlinear filtering problem, with discrete time and continuous time observation. We first present the method applied to the Fokker-Planck equation. The convergence of the approximation is established. We finally present a numerical example.

We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional ordinary differential equation. These two components are coupled with the bacterial consumption. Mechanisms...

In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system, and a finite volume method (based on an upwind implicit scheme) for the mean-field model. The finite...

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We propose a numerical approach to study the invasion fitness of a mutant and to determine evolutionary singular strategies in evolutionary structured models in which the competitive exclusion principle holds. Our approach is based on a dual representation, which consists of the modelling of the small size mutant population by a stochastic...

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Le modèle AM2b est classiquement représenté par un système d'équations différentielles. Toutefois ce modèle n'est valide qu'en grande population et notre objectif est d'établir plusieurs mo-dèles stochastiques à différentes échelles. À l'échelle microscopique, on propose un modèle sto-chastique de saut pur que l'on peut simuler de fa con...

We present two approaches to study invasion in growth-fragmentation-death mod- els. The first one is based on a stochastic individual based model, which is a piecewise deterministic branching process with a continuum of types, and the second one is based on an integro-differential model. The invasion of the population is described by the...

We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model, using a...

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Sequential Monte Carlo methods have been a major breakthrough in the field of numerical signal processing for stochastic dynamical state-space systems with partial and noisy observations. However, these methods still present certain weaknesses. One of the most fundamental is the degeneracy of the filter due to the impoverishment of the...

Sequential Monte Carlo methods have been a major breakthrough in the field of numerical signal processing for stochastic dynamical state-space systems with partial and noisy observations. However, these methods still present certain weaknesses. One of the most fundamental is the degeneracy of the filter due to the impoverishment of the...

Mixed affective states in bipolar disorder (BD) is a common psychiatric condition that occurs when symptoms of the two opposite poles coexist during an episode of mania or depression. A four-dimensional model by A. Goldbeter [27, 28] rests upon the notion that manic and depressive symptoms are produced by two competing and auto-inhibited neural...

Sequential Monte Carlo methods have been a major breakthrough in the field of numerical signal processing for stochastic dynamical state-space systems with partial and noisy observations. However, these methods still present certain weaknesses. One of the most fundamental is the degeneracy of the filter due to the impoverishment of the...

International audience