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UID:7066@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190412T110000
DTEND;TZID=Europe/Paris:20190412T120000
DTSTAMP:20241120T203410Z
URL:https://www.i2m.univ-amu.fr/evenements/convergence-of-feynman-kac-semi
 groups-and-large-deviations-of-diffusions-gregoire-ferre/
SUMMARY:Grégoire Ferré (Capital Fund Management (CFM)): Convergence of Fe
 ynman-Kac semigroups and large deviations of diffusions - Grégoire Ferré
DESCRIPTION:Grégoire Ferré: Feynman-Kac semigroups appear in various plac
 es of mathematics. They can be used in relation with rare events analysis\
 , or in quantum mechanics as a probabilistic representation of the ground 
 state. It is also an everyday tool in nonlinear filtering. Just like Marko
 v chains\, their long time behaviour is an important question\, be it for 
 theoretical or practical purposes.\n\nHowever\, the stability of such a dy
 namics is made difficult by its nonlinearity. We prove in [G.F.\, M. Rouss
 et in G. Stoltz\, 2018] that ergodic results can be obtained through assum
 ptions similar to that for Markov chains\, by performing a fine spectral a
 nalysis of the evolution operator. This shows an interesting competition b
 etween the dynamics itself and the weight given to its paths. As a by-prod
 uct\, we show [G.F.\, G. Stoltz\, in prep.] that the technique allows to d
 erive large deviations principles for empirical measures of diffusions in 
 Wasserstein topology\, which comes as a generalization of spectral gap con
 ditions for Witten-Laplacian operators in a non-symmetric setting.\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Gregoire_Ferre.jpg
CATEGORIES:Séminaire,Probabilités
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