Probabilistic Theory of Mean Field Games with Applications I Mean Fi
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, i
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René Carmona François Delarue
Probabilistic Theory of Mean Field Games with Applications I Mean Field FBSDEs, Control, and Games
Probability Theory and Stochastic Modelling Volume 83
Editors-in-chief Peter W. Glynn, Stanford, CA, USA Andreas E. Kyprianou, Bath, UK Yves Le Jan, Orsay, France Advisory Board Søren Asmussen, Aarhus, Denmark Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, Canada Halil Mete Soner, Zürich, Switzerland
The Probability Theory and Stochastic Modelling series is a merger and continuation of Springer’s two well established series Stochastic Modelling and Applied Probability and Probability and Its Applications series. It publishes research monographs that make a significant contribution to probability theory or an applications domain in which advanced probability methods are fundamental. Books in this series are expected to follow rigorous mathematical standards, while also displaying the expository quality necessary to make them useful and accessible to advanced students as well as researchers. The series covers all aspects of modern probability theory including • • • • • •
Gaussian processes Markov processes Random fields, point processes and random sets Random matrices Statistical mechanics and random media Stochastic analysis
as well as applications that include (but are not restricted to): • Branching processes and other models of population growth • Communications and processing networks • Computational methods in probability and stochastic processes, including simulation • Genetics and other stochastic models in biology and the life sciences • Information theory, signal processing, and image synthesis • Mathematical economics and finance • Statistical methods (e.g. empirical processes, MCMC) • Statistics for stochastic processes • Stochastic control • Stochastic models in operations research and stochastic optimization • Stochastic models in the physical sciences
More information about this series at http://www.springer.com/series/13205
René Carmona • François Delarue
Probabilistic Theory of Mean Field Games with Applications I Mean Field FBSDEs, Control, and Games
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René Carmona ORFE Department Program in Applied and Computational Mathematics Princeton University Princeton, NJ, USA
François Delarue Institut Universitaire de France & Laboratoire J.A. Dieudonné Université Nice Sophia Antipolis Nice, France
ISSN 2199-3130 ISSN 2199-3149 (electronic) Probability Theory and Stochastic Modelling ISBN 978-3-319-56437-1 ISBN 978-3-319-58920-6 (eBook) DOI 10.1007/978-3-319-58920-6 Library of Congress Control Number: 2017940988 Mathematics Subject Classification (2010): 91A13, 91A06, 91A55, 49N70, 49N90, 60H10, 60H15, 60H30 © Springer International Publishing AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the
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