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SUMMARY:Wenbin Yan
DTSTART:20260605T140000Z
DTEND:20260605T150000Z
DTSTAMP:20260604T063100Z
UID:indico-event-16449@indico.math.cnrs.fr
DESCRIPTION:Title:  Long-Time Behavior of Mean Field Game Systems with Co
 mmon White Noise\nContent: We study the long-time behavior of mean field g
 ame (MFG) systems driven by common noise\, providing a natural yet unexplo
 red extension of the deterministic MFG theory. In the deterministic settin
 g\, classical results establish convergence toward stationary solutions un
 der suitable monotonicity assumptions. The presence of common stochastic p
 erturbations\, however\, makes the analysis substantially more delicate. W
 e consider a standard MFG model with infinitely many players whose dynamic
 s are affected by both idiosyncratic and common noise\, and we investigate
  its asymptotic behavior as the time horizon tends to infinity. Using quan
 titative arguments that replace the compactness methods available in the d
 eterministic framework\, we prove exponential convergence of the solutions
  toward a stationary regime. More precisely\, we identify a deterministic 
 ergodic constant and show the existence of stationary random processes des
 cribing the limiting behavior. We also establish almost sure long-time con
 vergence through a detailed analysis of the ergodic master equation\, whic
 h governs the asymptotic behavior of the master equation.\nCo-Author(s) Pi
 erre Cardaliaguet\, Wenbin Yan\, Raphaël Maillet\n\nhttps://indico.math
 .cnrs.fr/event/16449/
LOCATION:Salle Olga Ladyjenskaïa (IHP - Bâtiment Borel)
URL:https://indico.math.cnrs.fr/event/16449/
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