m

F Nous contacter

0

Documents  Liverani, Carlangelo | enregistrements trouvés : 6

O
     

-A +A

P Q

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research talks;Partial Differential Equations;Probability and Statistics

We discuss some examples of the "good" effects of "very bad", "irregular" functions. In particular we will look at non-linear differential (partial or ordinary) equations perturbed by noise. By defining a suitable notion of "irregular" noise we are able to show, in a quantitative way, that the more the noise is irregular the more the properties of the equation are better. Some examples includes: ODE perturbed by additive noise, linear stochastic transport equations and non-linear modulated dispersive PDEs. It is possible to show that the sample paths of Brownian motion or fractional Brownian motion and related processes have almost surely this kind of irregularity. (joint work with R. Catellier and K. Chouk) We discuss some examples of the "good" effects of "very bad", "irregular" functions. In particular we will look at non-linear differential (partial or ordinary) equations perturbed by noise. By defining a suitable notion of "irregular" noise we are able to show, in a quantitative way, that the more the noise is irregular the more the properties of the equation are better. Some examples includes: ODE perturbed by additive noise, linear ...

35R60 ; 35Q53 ; 35D30 ; 60H15

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research talks;Partial Differential Equations;Probability and Statistics

We discuss the rough path principle and some of its applications to problems of homogenization.

60H15 ; 35B27

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research talks;Dynamical Systems and Ordinary Differential Equations;Probability and Statistics

It has long been observed that multi-scale systems, particularly those in climatology, exhibit behavior typical of stochastic models, most notably in the unpredictability and statistical variability of events. This is often in spite of the fact that the underlying physical model is completely deterministic. One possible explanation for this stochastic behavior is deterministic chaotic effects. In fact, it has been well established that the statistical properties of chaotic systems can be well approximated by stochastic differential equations. In this talk, we focus on fast-slow ODEs, where the fast, chaotic variables are fed into the slow variables to yield a diffusion approximation. In particular we focus on the case where the chaotic noise is multidimensional and multiplicative. The tools from rough path theory prove useful in this difficult setting. It has long been observed that multi-scale systems, particularly those in climatology, exhibit behavior typical of stochastic models, most notably in the unpredictability and statistical variability of events. This is often in spite of the fact that the underlying physical model is completely deterministic. One possible explanation for this stochastic behavior is deterministic chaotic effects. In fact, it has been well established that the ...

60H10 ; 37D20 ; 37D25 ; 37A50

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research talks;Partial Differential Equations;Probability and Statistics

35Q41 ; 60H15 ; 35R60

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research talks;Probability and Statistics

65C30 ; 60H10

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research talks;Dynamical Systems and Ordinary Differential Equations;Probability and Statistics

I will discuss the simplest possible (non trivial) example of a fast-slow partially hyperbolic system with particular emphasis on the problem of establishing its statistical properties.

37A25 ; 37C30 ; 37D30 ; 37A50 ; 60F17

... Lire [+]

Z