BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Florian Bechtold (Sorbonne Université - UPMC) DTSTART:20200615T130000Z DTEND:20200615T133000Z DTSTAMP:20260423T035731Z UID:LPDD/11 DESCRIPTION:Title: A law of large numbers for interacting diffusions via a mild formulation \nby Florian Bechtold (Sorbonne Université - UPMC) as part of Les probabi lités de demain webinar\n\n\nAbstract\nConsider a system of n weakly inte racting particles driven by independent Brownian motions. In many instance s\, it is well known that the empirical measure converges to the solution of a partial differential equation\, usually called McKean-Vlasov or Fokke r-Planck equation\, as n tends to infinity. We propose a relatively new ap proach to show this convergence by directly studying the stochastic partia l differential equation that the empirical measure satisfies for each fixe d n. Under a suitable control on the noise term\, which appears due to the finiteness of the system\, we are able to prove that the stochastic pertu rbation goes to zero\, showing that the limiting measure is a solution to the classical McKean-Vlasov equation. In contrast with known results\, we do not require any independence or finite moment assumption on the initial condition\, but the only weak convergence. The evolution of the empirical measure is studied in a suitable class of Hilbert spaces where the noise term is controlled using two distinct but complementary techniques: rough paths theory and maximal inequalities for self-normalized processes.\n LOCATION:https://researchseminars.org/talk/LPDD/11/ END:VEVENT END:VCALENDAR