Open Access
Volume 28, 2024
Page(s) 161 - 194
Published online 07 May 2024
  1. R. Buckdahn, J. Li, S. Peng and C. Rainer, Mean-field stochastic differential equations and associated pdes. Ann. Probab. 45 (2017) 824–878. [Google Scholar]
  2. J.-F. Chassagneux, D. Crisan and F. Delarue, A probabilistic approach to classical solutions of the master equation for large population equilibria. hal-01144845, 2015. [Google Scholar]
  3. R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications I, Vol. 83 of Probability Theory and Stochastic Modelling. Springer International Publishing (2018). [Google Scholar]
  4. N.V. Krylov, Controlled Diffusion Processes. Vol. 14 of Stochastic Modelling and Applied Probability. Springer (2009). [Google Scholar]
  5. V. Marx, Infinite-dimensional regularization of Mckean–Vlasov equation with a Wasserstein diffusion. arXiv:2002.10157, 2020. [Google Scholar]
  6. P.E. Caines, M. Huang and R.P. Malhamé, Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle. Commun. Inform. Syst. 6 (2006) 221–252. [Google Scholar]
  7. J.-M. Lasry and P.-L. Lions, Mean field games. Jap. J. Math. 2 (2007) 229–260. [Google Scholar]
  8. P.-L. Lions, Cours au Collège de France. [Google Scholar]
  9. P. Cardaliaguet, Notes on Mean Field Games, from P.L. Lions lectures at Collège de France (2010). [Google Scholar]
  10. R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications II, Vol. 84 of Probability Theory and Stochastic Modelling. Springer International Publishing (2018). [Google Scholar]
  11. A. Bensoussan, J. Frehse and S. Chi Phillip Yam, The master equation in mean field theory. J. Math. Pures Appl. 103 (2015) 1441–1474. [Google Scholar]
  12. R. Carmona and F. Delarue, The Master Equation for Large Population Equilibriums. Stochastic Analysis and Applications 2014. Springer (2014). [Google Scholar]
  13. P. Cardaliaguet, F. Delarue, J.-M. Lasry and P.L. Lions, The Master Equation and the Convergence Problem in Mean Field Games, Vol. 381 of AMS-201. Princeton University Press (2019). [Google Scholar]
  14. D. Crisan and E. McMurray, Smoothing properties of McKean–Vlasov SDEs. Probab. Theory Related Fields 171 (2017) 97–148. arXiv:1702.01397. [Google Scholar]
  15. C. Mou and J. Zhang, Wellposedness of second order master equations for mean field games with nonsmooth data. arXiv:1903.09907, 2020. [Google Scholar]
  16. P.-E. Chaudru de Raynal and N. Frikha, From the backward kolmogorov pde on the wasserstein space to propagation of chaos for mckean-vlasov sdes. J. Math. Pures Appl. 156 (2021) 1–124. [Google Scholar]
  17. P.-E. Chaudru de Raynal and N. Frikha, Well-posedness for some non-linear diffusion processes and related pde on the wasserstein space. J. Math. Pures Appl. (2021). [Google Scholar]
  18. F. Delarue and A. Tse, Uniform in time weak propagation of chaos on the torus. arXiv:2104.14973, 2021. [Google Scholar]
  19. J.-F. Chassagneux, L. Szpruch and A. Tse, Weak quantitative propagation of chaos via differential calculus on the space of measures. Ann. Appl. Probab. 32 (2022) 1929–1969. [Google Scholar]
  20. B. Jourdain and A. Tse, Central limit theorem over non-linear functionals of empirical measures with applications to the mean-field fluctuation of interacting particle systems. Electron. J. Probab. 26 (2021). [Google Scholar]
  21. X. Guo, H. Pham and X. Wei, Ito’s formula for flow of measures on semimartingales. arXiv:2010.05288, 2020. [Google Scholar]
  22. M. Talbi, N. Touzi and J. Zhang, Dynamic programming equation for the mean field optimal stopping problem. arXiv:2103.05736, 2021. [Google Scholar]
  23. G. dos Reis and V. Platonov, Itô-Wentzell-Lions formula for measure dependent random fields under full and conditional measure flows. Potential Anal. (2022). [Google Scholar]
  24. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer New York (2010). [Google Scholar]
  25. P. Billingsley, Convergence of Probability Measures, 2nd edn. Wiley Series in Probability and Statistics. Probability and Statistics Section. Wiley (1999). [Google Scholar]
  26. W. Rudin, Real and Complex Analysis, 3rd edn. McGraw-Hill (1987). [Google Scholar]

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