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# Documents  60J60 | enregistrements trouvés : 4

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## Multi angle  An Hodgkin-Huxley neuron receiving a random periodic signal : ergodicity and estimation Thieullen, Michèle (Auteur de la Conférence) | CIRM (Editeur )

In this talk I will present a stochastic model for the excitability of a neuron in a network. The neuron described by an Hodgkin-Huxley type model receives from the network a random input which is a perturbation of a periodic deterministic signal. For such a model we study ergodicity properties. Then, we prove limit theorems in order to be able to estimate characteristics of the sequence of spiking times. This talk is based on a joint work with R. Hoepfner (Univ. Mainz) and E. Loecherbach (Univ. Cergy-Pontoise).

Hodgkin-Huxley model - ergodicity - limit theorems - estimation
In this talk I will present a stochastic model for the excitability of a neuron in a network. The neuron described by an Hodgkin-Huxley type model receives from the network a random input which is a perturbation of a periodic deterministic signal. For such a model we study ergodicity properties. Then, we prove limit theorems in order to be able to estimate characteristics of the sequence of spiking times. This talk is based on a joint work with ...

## Multi angle  The geometry of subelliptic diffusions Thalmaier, Anton (Auteur de la Conférence) | CIRM (Editeur )

We discuss hypoelliptic and subelliptic diffusions; the lectures include the following topics: Malliavin calculus; Hormander's theorem; smoothness of transition probabilities under Hormander's brackets condition; control theory and Stroock-Varadhan's support theorems; hypoelliptic heat kernel estimates; gradient estimates and Harnack type inequalities for subelliptic diffusion semi-groups; notions of curvature related to sub-Riemannian diffusions. We discuss hypoelliptic and subelliptic diffusions; the lectures include the following topics: Malliavin calculus; Hormander's theorem; smoothness of transition probabilities under Hormander's brackets condition; control theory and Stroock-Varadhan's support theorems; hypoelliptic heat kernel estimates; gradient estimates and Harnack type inequalities for subelliptic diffusion semi-groups; notions of curvature related to sub-Riemannian ...

## Multi angle  Internal diffusion-limited aggregation with random starting points Kozma, Gady (Auteur de la Conférence) | CIRM (Editeur )

We consider a model for a growing subset of a euclidean lattice (an "aggregate") where at each step one choose a random point from the existing aggregate, starts a random walk from that point, and adds the point of exit to the aggregate. We show that the limiting shape is a ball. Joint work with Itai Benjamini, Hugo Duminil-Copin and Cyril Lucas.

## Multi angle  The Metropolis Hastings algorithm: introduction and optimal scaling of the transient phase Jourdain, Benjamin (Auteur de la Conférence) | CIRM (Editeur )

We first introduce the Metropolis-Hastings algorithm. We then consider the Random Walk Metropolis algorithm on $R^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one dimensional law. It is well-known that, in the limit $n$ tends to infinity, starting at equilibrium and for an appropriate scaling of the variance and of the timescale as a function of the dimension $n$, a diffusive limit is obtained for each component of the Markov chain. We generalize this result when the initial distribution is not the target probability measure. The obtained diffusive limit is the solution to a stochastic differential equation nonlinear in the sense of McKean. We prove convergence to equilibrium for this equation. We discuss practical counterparts in order to optimize the variance of the proposal distribution to accelerate convergence to equilibrium. Our analysis confirms the interest of the constant acceptance rate strategy (with acceptance rate between 1/4 and 1/3). We first introduce the Metropolis-Hastings algorithm. We then consider the Random Walk Metropolis algorithm on $R^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one dimensional law. It is well-known that, in the limit $n$ tends to infinity, starting at equilibrium and for an appropriate scaling of the variance and of the timescale as a function of the dimension $n$, a diffusive limit is obtained ...

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