Dienstag, 27. April 2010

Kolloquiumsvortrag von Prof. Dr. Ian Melbourne

Titel des Vortrags: Convergence of fast-slow ODEs to stochastic differential equations

Am Montag, dem 03. Mai 2010 hält 

Prof. Dr. Ian Melbourne (University of Surrey)

um 16:45 Uhr im Hörsaal D2 einen Vortrag mit dem Thema

"Convergence of fast-slow ODEs to stochastic differential equations"

Zu dieser Veranstaltung sind alle Interessenten herzlich eingeladen.

Um 16:15 Uhr trifft man sich zur Begrüßung des Gastes bei Tee und Kaffee im Besprechungsraum D2.343.


A project started recently with Andrew Stuart investigates the convergence of certain deterministic systems to a stochastic differential equation. For (presently over-simplified) fast-slow systems, we prove, under very mild conditions on the fast variables, that the slow-variable solutions converge to solutions of a stochastic differential equation.

A major difference between our approach and related projects is that we do not rely on decay of correlations for the fast variables (decay of correlations for flows is a notoriously difficult and poorly understood problem). Instead we use invariance principles (a generalisation of the central limit theorem giving convergence to Brownian motion) and large deviation estimates which have been derived for a very large class of systems in collaboration with Matthew Nicol.


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