[EstudiantesMatemática] charlas la semana que viene

[Paola Bermolen]

Hola,

Las charlas serán en el salón de seminarios del instituto de ing. eléctrica.

Saludos
paola

> MARTES 6 DE DICIEMBRE 11:30hs: FACULTAD DE INGENIERÍA - SALÓN A CONFIRMAR.
>
> Título:  Scaling methods for stochastic networks.
> Prof. Mathieu Feuillet. This presentation is partly based on joint works 
> with (alphabetically)
> Th Bonald, A Proutiere, Ph. Robert.
>
> Resumen:
> It is usually quite difficult to study the behavior of a
> multi-dimensional Markov process describing the evolution of a
> stochastic network.
> When it exists, the equilibrium distribution of stochastic networks is
> not known apart from some specific classes of processes. Moreover,
> even when this distribution is known, the dynamics of interest may not
> be the equilibrium. Some insight into the behavior of these networks
> can nevertheless be obtained through limit procedures which can be
> roughly described as follows: for some system parameter N, with an
> appropriate scaling, when N tends to infinity, the evolution of the
> state of the network converges to a much simpler process.
> After an introduction to some classical scaling methods, we give
> several illustrative examples and emphasize the difficulties due to
> border effects. We explain some techniques used to deal with these
> difficulties including notably Skorokhod problems and stochastic
> averaging.
>
>
> JUEVES 8 DE DICIEMBRE 11:30hs: FACULTAD DE INGENIERÍA - SALÓN A CONFIRMAR.
>
> Título: Martingale methods for computing hitting times in the
> Ehrenfest and Engset models.
> Prof. Mathieu Feuillet.  Joint work with Philippe Robert.
>
> Resumen:
> Martingale methods are a powerful tool to investigate the transient
> behavior of certain stochastic systems. For instance, many results on
> random walks and Brownian motion have been obtained thanks to
> exponential martingales. In this talk, we consider two classical
> stochastic processes, the Ehrenfest process, introduced in 1907 in the
> kinetic theory of gases to describe the heat exchange between two
> bodies and the Engset process, one of the early (1918) stochastic
> models of communication networks. We explain how to obtain a certain
> familiy of simple non-negative martingales and we derivate the Laplace
> transform of hitting times for both models. Finally, using standard
> analysis tools, we investigate the asymptotic behavior of the
> distributions of hitting times of these two processes when the number
> of particles/sources goes to infinity.
>
>
>
>