A general characterization of the mean field limit for stochastic differential games

Keywords

Mathematics, Limit (mathematics), Nash equilibrium, Infinity, Stochastic differential equation

References

• Mean Field Games and Mean Field Type Control TheoryAlain Bensoussan, Jens Frehse, Sheung Chi Phillip Yam — 2013
• Multidimensional Diffusion ProcessesDaniel W. Stroock, S. R. Srinivasa Varadhan — 1979
• Topics in Optimal TransportationCédric Villani — 2003
• Wellposedness of Mean Field Games with Common Noise under a Weak Monotonicity ConditionSaran Ahuja — 2014
• Mean field games with common noiseRené Carmona, François Delarue, Daniel Lacker — 2014
• Linear-Quadratic Mean Field GamesAlain Bensoussan, K. C. J. Sung, Sheung Chi Phillip Yam — 2014
• Probabilistic Analysis of Mean-Field GamesRené Carmona, François Delarue — 2012
• Mean Field Games Models—A Brief SurveyDiogo A. Gomes, João Saúde — 2013
• Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principlePeter E. Caines, Minyi Huang, Roland P. Malhamé — 2006
• Explicit solutions of some linear-quadratic mean field gamesMartino Bardi — 2012
• Mean Field Games and Systemic RiskRené Carmona, Jean‐Pierre Fouque, Li‐Hsien Sun — 2013
• LQG mean-field games with ergodic costMartino Bardi, Fabio S. Priuli — 2013
• Ecole d'été de probabilités de Saint-Flour XIX, 1989Donald L. Burkholder, Étienne Pardoux, Alain‐Sol Sznitman — 1991
• TOPICS IN OPTIMAL TRANSPORTATION (Graduate Studies in Mathematics 58) By CÉDRIC VILLANI: 370 pp., US$59.00, ISBN 0-8218-3312-X (American Mathematical Society, Providence, RI, 2003)G. R. Burton — 2004
• Existence of optimal controlsA. W. J. Stoddart — 1967
• A Martingale Approach to the Law of Large Numbers for Weakly Interacting Stochastic ProcessesKarl Oelschläger — 1984
• Jeux à champ moyen. I – Le cas stationnaireJean‐Michel Lasry, Pierre‐Louis Lions — 2006
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• Mean field gamesJean‐Michel Lasry, Pierre-Louis Lions — 2007
• Weak Limit Theorems for Stochastic Integrals and Stochastic Differential EquationsThomas G. Kurtz, Philip Protter — 1991

Cited by

• On mean field games with common noise and McKean-Vlasov SPDEsVassili N. Kolokoltsov, Marianna Troeva — 2015
• Translation invariant mean field games with common noiseDaniel Lacker, Kevin Webster — 2014
• CLASSICAL SOLUTIONS TO THE MASTER EQUATION FOR LARGE POPULATION EQUILIBRIAJean-François Chassagneux, Dan Crisan, François Delarue — 2014
• Wellposedness of Mean Field Games with Common Noise under a Weak Monotonicity ConditionSaran Ahuja — 2014
• On Solutions of Mean Field Games with Ergodic CostAri Arapostathis, Anup Biswas, Johnson Carroll — 2015
• Mean field games via controlled martingale problems: Existence of Markovian equilibriaDaniel Lacker — 2014
• Deterministic Limit of Mean Field Games Associated with Nonlinear Markov ProcessesYurii Averboukh — 2015
• A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population EquilibriaJean-François Chassagneux, Dan Crisan, François Delarue — 2014
• Endogenous Formation of Limit Order Books: the Effects of Trading FrequencyRoman Gayduk, Sergey Nadtochiy — 2015
• Existence of Weak Solutions to Stationary Mean-Field Games through Variational InequalitiesRita Ferreira, Diogo A. Gomes — 2015
• Homogenization of a Mean Field Game System in the Small Noise LimitAnnalisa Cesaroni, Nicolas Dirr, Claudio Marchi — 2016
• Rate control under heavy traffic with strategic serversErhan Bayraktar, Amarjit Budhiraja, Asaf Cohen — 2016
• A Mean Field Game of Optimal StoppingMarcel Nutz — 2016
• Endogenous Formation of Limit Order Books: Dynamics Between TradesRoman Gayduk, Sergey Nadtochiy — 2016
• Liquidity effects of trading frequencyRoman Gayduk, Sergey Nadtochiy — 2015
• Mean Field Games of Timing and Models for Bank RunsRené Carmona, François Delarue, Daniel Lacker — 2016
• Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible ResourceP. Jameson Graber — 2016
• Limit Theory for Controlled McKean-Vlasov DynamicsDaniel Lacker — 2016
• The Convergence Problem in Mean Field Games with Local CouplingP. Cardaliaguet — 2016
• Forward–backward stochastic differential equations with monotone functionals and mean field games with common noiseSaran Ahuja, Weiluo Ren, Tzu-Wei Yang — 2016

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