Bernoulli Lecture I: Mathematical Analysis of Stochastic Systems with Mean Field Interactions.
Event details
| Date | 15.03.2012 |
| Hour | 16:30 › 17:30 |
| Speaker | Rene Carmona, Princeton University |
| Location | |
| Category | Conferences - Seminars |
Problems in biology, population dynamics, statistical physics and economics often require high-dimensional mathematical models, and the search for effective equations exploiting invariance under symmetry groups is a time-honored method to reduce the complexity and provide reasonable approximations.
Motivated by the recent works of Lasry and Lions on approximate Nash equilibrium for Mean Field Games, we present an application of these
ideas to the theory of systems of stochastic differential equations with mean field interactions.
After a brief review of the challenges raised by the systems of forward and backward partial differential equations introduced by Lasry and Lions, we discuss a probabilistic alternative and present solvable models. The proofs rely on a stochastic version of the Pontryagin maximum principle, the introduction of an appropriate notion of differentiability for functions of measures, and fixed point arguments already present in Sznitman's analysis of the McKean-Vlasov equation and the propagation of chaos.
Motivated by the recent works of Lasry and Lions on approximate Nash equilibrium for Mean Field Games, we present an application of these
ideas to the theory of systems of stochastic differential equations with mean field interactions.
After a brief review of the challenges raised by the systems of forward and backward partial differential equations introduced by Lasry and Lions, we discuss a probabilistic alternative and present solvable models. The proofs rely on a stochastic version of the Pontryagin maximum principle, the introduction of an appropriate notion of differentiability for functions of measures, and fixed point arguments already present in Sznitman's analysis of the McKean-Vlasov equation and the propagation of chaos.
Practical information
- General public
- Free
Organizer
- DALANG Robert (EPFL).
DOZZI Marco (Université de Nancy).
FLANDOLI Franco (University of Pisa).
RUSSO Francesco (ENSTA ParisTech).
Contact
- Rana Gherzeddine