The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Abstract:
Since its introduction by P.L. Lions in his lectures and seminars at the College de France, see also the very helpful notes of Cardialaguet on Lions' lectures, the Master equation has attracted a lot of interest, and various points of view have been expressed, see Carmona-Delarue, Bensoussan-Frehse-Yam , Buckdahn-Li-Peng-Rainer . There are several ways to introduce this type of equation. It involves an argument which is a probability measure, and P.L. Lions has proposed the idea of working with the Hilbert space of random variables which are square integrable. So writing the equation is an issue. Another issue is its origin. We discuss in this paper these various aspects, and for the modeling rely heavily on a seminar at College de France delivered by P.L. Lions on November 14, 2014.
References
- Bensoussan A.,Frehse J. , Yam P., (2014) The Master Equation In Mean Field Theory , Journal de Mathématiques Pures et Appliquées , Paris
- Buckdahn R., Li J., Peng SG, Rainer C. (2014) Mean Field stochastic differential equations and associated PDEs, preprint
- Cardaliaguet P., (2013) Notes on P.L. Lions' lectures at the College de France, Working Paper, september
- Carmona R., Delarue F., (2014) The Master Equation for Large Population Equilibriums, Arxiv, may
- Lions P.L., Lectures at College de France, http://www.college-de-france.fr
- Lions P.L., (2014) Seminar at College de France, November 14
Biography:
Alain Bensoussan is Ashbel Smith Professor and the Director of ICDRiA (International Center for Decision and Risk Analysis) at the University of Texas at Dallas. He is also Chair Professor of Risk and Decision Analysis at the City University Hong Kong. He is Professor Emeritus at the University Paris Dauphine.
Professor Bensoussan served as President of National Institute for Research in Computer Science and Control (INRIA) from 1984 to 1996; President of the French Space Agency (CNES) from 1996 to 2003; and Chairman of the European Space Agency (ESA) Council from 1999 to 2002. He was World Class University Distinguished Professor at Ajou University, from 2010 to 2013. He is a member of the French Academy of Sciences, French Academy of Technology, Academia Europae, and International Academy of Astronautics. His distinctions include AMS Fellow, IEEE Fellow, SIAM Fellow, Von Humboldt award, and the NASA public service medal. Professor Bensoussan is a decorated Officer of Legion d’Honneur , Commandeur Ordre National du Merite and Officer Bundes Verdienst Kreuz.