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SUMMARY:Error estimates of a theta-scheme for second-order mean field game
 s
DTSTART:20230609T133000Z
DTEND:20230609T143000Z
DTSTAMP:20260610T152500Z
UID:indico-event-9942@indico.math.cnrs.fr
DESCRIPTION:Speakers: Kang LIU (Ecole Polytechnique)\n\nWe introduce and a
 nalyze a new finite-difference scheme\, relying on the theta-method\, for 
 solving monotone second-order mean field games. These games consist of a c
 oupled system of the Fokker-Planck and the Hamilton-Jacobi-Bellman equatio
 n. The theta-method is used for discretizing the diffusion terms: we appro
 ximate them with a convex combination of an implicit and an explicit term.
  On contrast\, we use an explicit centered scheme for the first-order term
 s. Assuming that the running cost is strongly convex and regular\, we firs
 t prove the monotonicity and the stability of our theta-scheme\, under a C
 FL condition. Taking advantage of the regularity of the solution of the co
 ntinuous problem\, we estimate the consistency error of the theta-scheme. 
 Our main result is a convergence rate of order $O(h^r)$ for the theta-sche
 me\, where $h$ is the step length of the space variable and $r \\in (0\,1)
 $ is related to the Hölder continuity of the solution of the continuous p
 roblem and some of its derivatives.\n\nhttps://indico.math.cnrs.fr/event/9
 942/
LOCATION:Salle 421 (Institut Henri Poincaré)
URL:https://indico.math.cnrs.fr/event/9942/
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