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SUMMARY:Bernoulli Lecture I: Mathematical Analysis of Stochastic Systems w
 ith Mean Field Interactions. 
DTSTART:20120315T163000
DTEND:20120315T173000
DTSTAMP:20260916T061201Z
UID:4fc5fceff63a11d2a10a851935964c9c70c322c7f504c456b8430919
CATEGORIES:Conferences - Seminars
DESCRIPTION:Rene Carmona\, Princeton University\nProblems in biology\, pop
 ulation dynamics\, statistical physics and economics often require high-di
 mensional mathematical models\, and the search for effective equations exp
 loiting invariance under symmetry groups is a time-honored method to reduc
 e the complexity and provide reasonable approximations.\n\nMotivated by th
 e recent works of Lasry and Lions on approximate Nash equilibrium for Mean
  Field Games\, we present an application of these\nideas to the theory of 
 systems of stochastic differential equations with mean field interactions.
 \n\nAfter a brief review of the challenges raised by the systems of forwar
 d and backward partial differential equations introduced by Lasry and Lion
 s\, we discuss a probabilistic alternative and present solvable models. Th
 e proofs rely on a stochastic version of the Pontryagin maximum principle\
 , the introduction of an appropriate notion of differentiability for funct
 ions of measures\, and fixed point arguments already present in Sznitman's
  analysis of the McKean-Vlasov  equation and the propagation of chaos.
LOCATION:SV 1717 https://plan.epfl.ch/?room==SV%201717
STATUS:CONFIRMED
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