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UID:3332@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140418T110000
DTEND;TZID=Europe/Paris:20140418T120000
DTSTAMP:20210125T142759Z
URL:https://www.i2m.univ-amu.fr/events/sobolev-inequality-and-the-invarian
ce-principle-for-diffusions-in-periodic-potential-moustapha-ba/
SUMMARY:Sobolev inequality and the invariance principle for diffusions in p
eriodic potential - Moustapha Ba - Moustapha Ba
DESCRIPTION:We prove here\, using stochastic analysis methods \; the invari
ance principle for a Rd- diffusions d ≥ 2 \; involving in periodic poten
tial beyond uniform boundedness assumptions and beyond regularity assumpti
ons on potential. The potential is not assumed to have any regularity. So
the stochastic calculus theory for processes associated to Dirichlet forms
used to justify the existence of this process starting for almost all x
∈ Rd. We show by using harmonic analysis ? one Sobolev inequality with d
ifferent weight to bound the probability of transition associated to the t
ime changed diffusion for all times and deduce the existence of one bounde
d density. This property allows us to prove easily the tightness of the se
quence of processes in the uniform topology. The proof of the con- vergenc
e in finite dimensional distribution is very standard: construction and co
nvergence of the so-called corrector ? and central limit theorem for marti
ngale with continuous time (Helland 1982). The approach used here is the s
ame as in [2] (Mathieu 2008): the notion of time changed process by an add
itive functional.\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
014/04/Moustapha_Ba.jpg
CATEGORIES:Séminaire Probabilités
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