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UID:8392@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140418T110000
DTEND;TZID=Europe/Paris:20140418T120000
DTSTAMP:20241120T210359Z
URL:https://www.i2m.univ-amu.fr/evenements/sobolev-inequality-and-the-inva
 riance-principle-for-diffusions-in-periodic-potential-moustapha-ba/
SUMMARY:Moustapha Ba (I2M\, Aix-Marseille Université): Sobolev inequality 
 and the invariance principle for diffusions in periodic potential - Mousta
 pha Ba
DESCRIPTION:Moustapha Ba: We prove here\, using stochastic analysis methods
  \; the invariance principle for a Rd- diffusions d ≥ 2 \; involving in 
 periodic potential beyond uniform boundedness assumptions and beyond regul
 arity assumptions on potential. The potential is not assumed to have any r
 egularity. So the stochastic calculus theory for processes associated to D
 irichlet forms used to justify the existence of this process starting for 
 almost all x ∈ Rd. We show by using harmonic analysis ? one Sobolev ineq
 uality with different weight to bound the probability of transition associ
 ated to the time changed diffusion for all times and deduce the existence 
 of one bounded density. This property allows us to prove easily the tightn
 ess of the sequence of processes in the uniform topology. The proof of the
  con- vergence in finite dimensional distribution is very standard: constr
 uction and convergence of the so-called corrector ? and central limit theo
 rem for martingale with continuous time (Helland 1982). The approach used 
 here is the same as in [2] (Mathieu 2008): the notion of time changed proc
 ess by an additive 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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