[EstudiantesMatemática]Invitación a charlas de Mathieu Feuillet

[Nicolás Frevenza]

Hola, les estoy reenviando invitaciones a dos charlas que dará el
profesor Mathieu Feuillet del INRIA durante esta semana, en el marco de una
visita de trabajo que se realiza con el apoyo del IFUM.

Saludos

Nicolás

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*MARTES 6 DE DICIEMBRE 11:30hs: FACULTAD DE INGENIERÍA (en el Instituto de
Ingeniería Eléctrica).*

*Título: *Scaling methods for stochastic networks.
*Expositor:* Prof. Mathieu Feuillet (INRIA)

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 (en el Instituto de
Ingeniería Eléctrica).*

*Título:* Martingale methods for computing hitting times in the Ehrenfest
and Engset models.
*Expositor:* Prof. Mathieu Feuillet. (INRIA)
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.
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